In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k compon...In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k components, 2d1-cycle, ⋯, 2dk-cycle, if one of the following is satisfied: (1) k=2, δ(G)≥2and d1−2≥d2≥2;(2) k=3, δ(G)≥d3+2and d1−2≥d2≥d3≥4. In particular, this extends one result of Moon and Moser in 1963 under condition (1).展开更多
This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i...This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.展开更多
Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G ...Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.展开更多
Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H i...Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, .展开更多
In this paper, we analyze US stock market with a new 5-factor model in Zhou and Li (2016) [1]. Data we use are 48 industry portfolios (Jul. 1963-Jan. 2017). Parameters are estimated by MLE. LR and KS are used for mode...In this paper, we analyze US stock market with a new 5-factor model in Zhou and Li (2016) [1]. Data we use are 48 industry portfolios (Jul. 1963-Jan. 2017). Parameters are estimated by MLE. LR and KS are used for model diagnostics. Model comparison is done with AIC. The results show Fama-French 5 factors are still alive. This new model in Zhou and Li (2016) [1] fits the data better than the one in Fama and French (2015) [2].展开更多
In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of ...In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.展开更多
In this paper, we empirically test a new model with the data of US services sector, which is an extension of the 5-factor model in Fama and French (2015) [1]. 3 types of 5 factors (Global, North American and US) are c...In this paper, we empirically test a new model with the data of US services sector, which is an extension of the 5-factor model in Fama and French (2015) [1]. 3 types of 5 factors (Global, North American and US) are compared. Empirical results show the Fama-French 5 factors are still alive! The new model has better in-sample fit than the 5-factor model in Fama and French (2015).展开更多
Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connec...Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.展开更多
Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we ...Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we provide a tight spectral radius condition for a graph to have(a,b)-parity factors.展开更多
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f betwo integer-valued functions defined on V(G) such that 2k - 2 ≤ g(x) ≤ f(x) for all x ∈ V(G).Let H be a subgraph of G with mk edges. In this...Let G be a graph with vertex set V(G) and edge set E(G) and let g and f betwo integer-valued functions defined on V(G) such that 2k - 2 ≤ g(x) ≤ f(x) for all x ∈ V(G).Let H be a subgraph of G with mk edges. In this paper, it is proved that every (mg + m - 1, mf - m +l)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions.展开更多
Kinetic parameters of the decomposition of hazardous chemicals can be applied for the estimation of their thermal behavior under any temperature profile.Presented paper describes the application of the advanced kineti...Kinetic parameters of the decomposition of hazardous chemicals can be applied for the estimation of their thermal behavior under any temperature profile.Presented paper describes the application of the advanced kinetic approach for the determination of the thermal behavior also under adiabatic conditions occurring e.g.in batch reactors in case of cooling failure.The kinetics of the decomposition of different samples(different manufacturers and batches) of 3-methyl-4-nitrophenol were investigated by conventional DSC in non-isothermal(few heating rates varying from 0.25 to 8.0K/min) and isothermal(range of 200~260℃) modes.The kinetic parameters obtained with AKTS-Thermokinetics Software were applied for calculating reaction rate and progress under different heating rates and temperatures and verified by comparing simulated and experimental signals.After application of the heat balance to compare the amount of heat generated during reaction and its removal from the system,the knowledge of reaction rate at any temperature profiles allowed the determination of the temperature increase due to the self-heating in adiabatic and pseudo-adiabatic conditions.Applied advanced kinetic approach allowed simulation the course of the Heat-Wait-Search(HWS) mode of operation of adiabatic calorimeters.The thermal safety diagram depicting dependence of Time to Maximum Rate(TMR) on the initial temperature was calculated and compared with the results of HWS experiments carried out in the system with Ф-factor amounting to 3.2.The influence of the Ф-factor and reaction progress reached at the end of the HWS monitoring on the TMR is discussed.Presented calculations clearly indicate that even very minor reaction progress reduces the TMRad of 24h characteristic for a sample with initial reaction progress amounting to zero.Described estimation method can be verified by just one HWS-ARC,or by one correctly chosen ISO-ARC run of reasonable duration by knowing in advance the dependence of the TMR on the initial temperature for any Ф-factor.Proposed procedure results in significant shortening of the measuring time compared to a safety hazard approach based on series of ARC experiments carried out at the beginning of a process safety evaluation.展开更多
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k-1≤g(x) ≤ f(x) for all x ∈ V(G). Let H be a subgraph of G with mk edges . In this ...Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k-1≤g(x) ≤ f(x) for all x ∈ V(G). Let H be a subgraph of G with mk edges . In this paper it is proved that every (mg + m - 1,mf- m + 1)-graph G has (g, f)-factorizations randomly κ-orthogonal to H and shown that the result is best possible.展开更多
Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjec...Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjectured that for any k independent edges e1,……, ek of G, G has a 2-factor with k cycles C1, C2, ……, Ck with respect to {e1, e2,……, ek} such that k - 1 of them are quadrilaterals. In this paper, we prove this conjecture.展开更多
Let G be a graph, and g, f ： V（G）→Z＋ with g（x） 〈 f（x） for each x ∈ V（G）. We say that G admits all fractional （g, f）-factors if G contains an fractional r-factor for every r ： V（G）→ Z＋ with g（x） ...Let G be a graph, and g, f ： V（G）→Z＋ with g（x） 〈 f（x） for each x ∈ V（G）. We say that G admits all fractional （g, f）-factors if G contains an fractional r-factor for every r ： V（G）→ Z＋ with g（x） ≤ r（x） ≤ f（x） for any x ∈ V（G）. Let H be a subgraph of G. We say that G has all fractional （g, f）-factors excluding H if for every r ： V（G） → Z＋ with g（x） ≤ r（x） ≤ f（x） for all x ∈ V（G）, G has a fractional r-factor Fh such that E（H） ∩ E（Fh） = Ф, where h ： E（G） → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional （g, f）-factors excluding H and obtain two sufficient conditions for a graph to have all fractional （g, f）-factors excluding H.展开更多
A spanning subgraph F of a graph G is called a path factor of G if each component of F is a path.A P≥k-factor means a path factor with each component having at least k vertices,where k≥2 is an integer.Bazgan,Benhamd...A spanning subgraph F of a graph G is called a path factor of G if each component of F is a path.A P≥k-factor means a path factor with each component having at least k vertices,where k≥2 is an integer.Bazgan,Benhamdine,Li and Wozniak[C.Bazgan,A.H.Benhamdine,H.Li,M.Wozniak,Partitioning vertices of 1-tough graph into paths,Theoret.Comput.Sci.263(2001)255–261.]obtained a toughness condition for a graph to have a P≥3-factor.We introduce the concept of a P≥k-factor deleted graph,that is,if a graph G has a P≥k-factor excluding e for every e∈E(G),then we say that G is a P≥k-factor deleted graph.In this paper,we show four sufficient conditions for a graph to be a P≥3-factor deleted graph.Furthermore,it is shown that four results are best possible in some sense.展开更多
Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a...Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a＋2 b＋a（r-1）and ｜NG（x1） ∪ NG（x2） ∪…∪ NG（xr）｜ ≥（a＋b）n/（a＋2 b） for any independent subset {x1,x2,…,xr} in G. It is a generalization of Zhou et al.＇s previous result [Discussiones Mathematicae Graph Theory, 36： 409-418（2016）]in which r = 2 is discussed. Furthermore, we show that this result is best possible in some sense.展开更多
Let a,b and k be nonnegative integers with a≥2 and b≥a(k+1)+2.A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle.A graph G is said to hav...Let a,b and k be nonnegative integers with a≥2 and b≥a(k+1)+2.A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle.A graph G is said to have a k-Hamiltonian[a,b]-factor if after deleting any k vertices of G the remaining graph of G admits a Hamiltonian[a,b]-factor.Let G is a k-Hamiltonian graph of order n with n≥a+k+2.In this paper,it is proved that G contains a k-Hamiltonian[a,b]-factor ifδ(G)≥a+k andδ(G)≥I(G)≥a-1+(a(k+1))/(b-2).展开更多
文摘In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k components, 2d1-cycle, ⋯, 2dk-cycle, if one of the following is satisfied: (1) k=2, δ(G)≥2and d1−2≥d2≥2;(2) k=3, δ(G)≥d3+2and d1−2≥d2≥d3≥4. In particular, this extends one result of Moon and Moser in 1963 under condition (1).
基金This work is supported by NNSF of ChinaRFDP of Higher Education
文摘This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.
基金This work was supported by NNSF. RFDP and NNSF of shandong province(Z2000A02 ).
文摘Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.
文摘Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, .
文摘In this paper, we analyze US stock market with a new 5-factor model in Zhou and Li (2016) [1]. Data we use are 48 industry portfolios (Jul. 1963-Jan. 2017). Parameters are estimated by MLE. LR and KS are used for model diagnostics. Model comparison is done with AIC. The results show Fama-French 5 factors are still alive. This new model in Zhou and Li (2016) [1] fits the data better than the one in Fama and French (2015) [2].
基金This work is supported by NSFC (10471078.10201019)RSDP (20040422004) of China
文摘In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.
文摘In this paper, we empirically test a new model with the data of US services sector, which is an extension of the 5-factor model in Fama and French (2015) [1]. 3 types of 5 factors (Global, North American and US) are compared. Empirical results show the Fama-French 5 factors are still alive! The new model has better in-sample fit than the 5-factor model in Fama and French (2015).
基金Supported by the National Natural Science Foundation of China( 60 1 72 0 0 3) NSF of Shandongprovince ( Z2 0 0 0 A0 2 )
文摘Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.
文摘Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we provide a tight spectral radius condition for a graph to have(a,b)-parity factors.
基金The work is partially supported by NNSF of China(10471078)RSDP of China
文摘Let G be a graph with vertex set V(G) and edge set E(G) and let g and f betwo integer-valued functions defined on V(G) such that 2k - 2 ≤ g(x) ≤ f(x) for all x ∈ V(G).Let H be a subgraph of G with mk edges. In this paper, it is proved that every (mg + m - 1, mf - m +l)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions.
文摘Kinetic parameters of the decomposition of hazardous chemicals can be applied for the estimation of their thermal behavior under any temperature profile.Presented paper describes the application of the advanced kinetic approach for the determination of the thermal behavior also under adiabatic conditions occurring e.g.in batch reactors in case of cooling failure.The kinetics of the decomposition of different samples(different manufacturers and batches) of 3-methyl-4-nitrophenol were investigated by conventional DSC in non-isothermal(few heating rates varying from 0.25 to 8.0K/min) and isothermal(range of 200~260℃) modes.The kinetic parameters obtained with AKTS-Thermokinetics Software were applied for calculating reaction rate and progress under different heating rates and temperatures and verified by comparing simulated and experimental signals.After application of the heat balance to compare the amount of heat generated during reaction and its removal from the system,the knowledge of reaction rate at any temperature profiles allowed the determination of the temperature increase due to the self-heating in adiabatic and pseudo-adiabatic conditions.Applied advanced kinetic approach allowed simulation the course of the Heat-Wait-Search(HWS) mode of operation of adiabatic calorimeters.The thermal safety diagram depicting dependence of Time to Maximum Rate(TMR) on the initial temperature was calculated and compared with the results of HWS experiments carried out in the system with Ф-factor amounting to 3.2.The influence of the Ф-factor and reaction progress reached at the end of the HWS monitoring on the TMR is discussed.Presented calculations clearly indicate that even very minor reaction progress reduces the TMRad of 24h characteristic for a sample with initial reaction progress amounting to zero.Described estimation method can be verified by just one HWS-ARC,or by one correctly chosen ISO-ARC run of reasonable duration by knowing in advance the dependence of the TMR on the initial temperature for any Ф-factor.Proposed procedure results in significant shortening of the measuring time compared to a safety hazard approach based on series of ARC experiments carried out at the beginning of a process safety evaluation.
基金the National Natural Science Foundation of China (No.60172003,19831080) by NSF of Shandong Province.
文摘Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k-1≤g(x) ≤ f(x) for all x ∈ V(G). Let H be a subgraph of G with mk edges . In this paper it is proved that every (mg + m - 1,mf- m + 1)-graph G has (g, f)-factorizations randomly κ-orthogonal to H and shown that the result is best possible.
基金NNSF of China(10471078)Higher Education of MOE,P.R.C.(2004042204)
文摘Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjectured that for any k independent edges e1,……, ek of G, G has a 2-factor with k cycles C1, C2, ……, Ck with respect to {e1, e2,……, ek} such that k - 1 of them are quadrilaterals. In this paper, we prove this conjecture.
基金supported by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)sponsored by Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Province
文摘Let G be a graph, and g, f ： V（G）→Z＋ with g（x） 〈 f（x） for each x ∈ V（G）. We say that G admits all fractional （g, f）-factors if G contains an fractional r-factor for every r ： V（G）→ Z＋ with g（x） ≤ r（x） ≤ f（x） for any x ∈ V（G）. Let H be a subgraph of G. We say that G has all fractional （g, f）-factors excluding H if for every r ： V（G） → Z＋ with g（x） ≤ r（x） ≤ f（x） for all x ∈ V（G）, G has a fractional r-factor Fh such that E（H） ∩ E（Fh） = Ф, where h ： E（G） → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional （g, f）-factors excluding H and obtain two sufficient conditions for a graph to have all fractional （g, f）-factors excluding H.
基金supported by Six Talent Peaks Project in Jiangsu Province,China(Grant No.JY–022)。
文摘A spanning subgraph F of a graph G is called a path factor of G if each component of F is a path.A P≥k-factor means a path factor with each component having at least k vertices,where k≥2 is an integer.Bazgan,Benhamdine,Li and Wozniak[C.Bazgan,A.H.Benhamdine,H.Li,M.Wozniak,Partitioning vertices of 1-tough graph into paths,Theoret.Comput.Sci.263(2001)255–261.]obtained a toughness condition for a graph to have a P≥3-factor.We introduce the concept of a P≥k-factor deleted graph,that is,if a graph G has a P≥k-factor excluding e for every e∈E(G),then we say that G is a P≥k-factor deleted graph.In this paper,we show four sufficient conditions for a graph to be a P≥3-factor deleted graph.Furthermore,it is shown that four results are best possible in some sense.
基金supported by the National Natural Science Foundation of China(Nos.11371052,11731002)the Fundamental Research Funds for the Central Universities(Nos.2016JBM071,2016JBZ012)the 111 Project of China(B16002)
文摘Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a＋2 b＋a（r-1）and ｜NG（x1） ∪ NG（x2） ∪…∪ NG（xr）｜ ≥（a＋b）n/（a＋2 b） for any independent subset {x1,x2,…,xr} in G. It is a generalization of Zhou et al.＇s previous result [Discussiones Mathematicae Graph Theory, 36： 409-418（2016）]in which r = 2 is discussed. Furthermore, we show that this result is best possible in some sense.
基金supported by the National Natural Science Foundation of China (Grant No. 11371009)the National Social Science Foundation of China (Grant No. 14AGL001)+1 种基金sponsored by Six Big Talent Peak of Jiangsu Province (Grant No. JY–022)333 Project of Jiangsu Province
文摘Let a,b and k be nonnegative integers with a≥2 and b≥a(k+1)+2.A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle.A graph G is said to have a k-Hamiltonian[a,b]-factor if after deleting any k vertices of G the remaining graph of G admits a Hamiltonian[a,b]-factor.Let G is a k-Hamiltonian graph of order n with n≥a+k+2.In this paper,it is proved that G contains a k-Hamiltonian[a,b]-factor ifδ(G)≥a+k andδ(G)≥I(G)≥a-1+(a(k+1))/(b-2).
