Pilsniak and Wozniak put forward the concept of neighbor sum distinguishing(NSD)total coloring and conjectured that any graph with maximum degreeΔadmits an NSD total(Δ+3)-coloring in 2015.In 2016,Qu et al.showed tha...Pilsniak and Wozniak put forward the concept of neighbor sum distinguishing(NSD)total coloring and conjectured that any graph with maximum degreeΔadmits an NSD total(Δ+3)-coloring in 2015.In 2016,Qu et al.showed that the list version of the conjecture holds for any planar graph withΔ≥13.In this paper,we prove that any planar graph withΔ≥7 but without 6-cycles satisfies the list version of the conjecture.展开更多
A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform ...A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform if all its hyperedges have the same size k,and H is L-intersecting if the number of common vertices of every two hyperedges belongs to L.In this paper,we propose and investigate the problem of estimating the maximum k among all k-uniform L-intersecting(n,m)-hypergraphs for fixed n,m and L.We will provide some tight upper and lower bounds on k in terms of n,m and L.展开更多
Let Η be a hypergraph with n vertices. Suppose that di,¢/2,...,dn are degrees of the vert ices of Η. The t-th graph entropy based on degrees of H is defined as Id^t(Η)=-n∑i=1(di^t/∑j=1^ndj^t^nlogdi^t/∑j=1^ndj^t...Let Η be a hypergraph with n vertices. Suppose that di,¢/2,...,dn are degrees of the vert ices of Η. The t-th graph entropy based on degrees of H is defined as Id^t(Η)=-n∑i=1(di^t/∑j=1^ndj^t^nlogdi^t/∑j=1^ndj^t^n)=log(n∑i=1di^t)-n∑i=1(di^t/∑j=1^ndj^tlogdi^t), where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of Id^t(Η) for t = 1, when Η is among all uniform super trees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.展开更多
A graph is called claw-free if it contains no induced subgrapn lsomorpmc to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least ([V(G)I - 2...A graph is called claw-free if it contains no induced subgrapn lsomorpmc to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least ([V(G)I - 2)/3. At the workshop CSzC (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z1 (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if eachend-vertex of every induced copy of H in G has degree at least IV(G)I/3 + 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.end-vertex of every induced copy of H in G has degree at least IV(G)I/3 + 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.展开更多
In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, w...In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, we derive a result which strengthens substantially the well- known theorem on set systems with k-wise E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 (2004)]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.展开更多
Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamil- tonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other ...Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamil- tonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.展开更多
Let G be a bridgeless graph and C be a circuit in G.To find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp...Let G be a bridgeless graph and C be a circuit in G.To find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp(f)∩E(C)|>3/4|E(C)|,and showed that the conjecture holds if|E(C)|≤19[Combinatorica,37,1097–1112(2017)].In this paper,we prove that the conjecture holds if|E(C)|≤27.展开更多
In this paper,we give some sufficient conditions for extended neighborhood coronas to have Laplacian perfect state transfer.We also give some conditions for extended neighborhood coronas to be periodic.
In this paper, we discuss the connection between the rigid graded selfduality over some noncommutative graded ring and the selfduality over its initial subring.
基金Supported by National Natural Science Foundation of China(Grant Nos.11871397,11671320 and U1803263)the Fundamental Research Funds for the Central Universities(Grant No.3102019ghjd003)+1 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2020JM-083)Shangluo University Key Disciplines Project(Discipline name Mathematics)。
文摘Pilsniak and Wozniak put forward the concept of neighbor sum distinguishing(NSD)total coloring and conjectured that any graph with maximum degreeΔadmits an NSD total(Δ+3)-coloring in 2015.In 2016,Qu et al.showed that the list version of the conjecture holds for any planar graph withΔ≥13.In this paper,we prove that any planar graph withΔ≥7 but without 6-cycles satisfies the list version of the conjecture.
基金Supported by National Natural Science Foundation of China(Grant Nos.12242111,12131013,12171393,12071370,71973103,U1803263,11601430)Natural Science Foundation of Shaanxi Province(Grant Nos.2021JM-040,2020JQ-099)+2 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSZ009)Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2023A1515030208,2022A1515010899)the Fundamental Research Funds for the Central Universities。
文摘A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform if all its hyperedges have the same size k,and H is L-intersecting if the number of common vertices of every two hyperedges belongs to L.In this paper,we propose and investigate the problem of estimating the maximum k among all k-uniform L-intersecting(n,m)-hypergraphs for fixed n,m and L.We will provide some tight upper and lower bounds on k in terms of n,m and L.
基金Supported by NSFC(Grant Nos.11531011,11671320,11601431,11871034 and U1803263)the China Postdoctoral Science Foundation(Grant No.2016M600813)the Natural Science Foundation of Shaanxi Province(Grant No.2017JQ1019)
文摘Let Η be a hypergraph with n vertices. Suppose that di,¢/2,...,dn are degrees of the vert ices of Η. The t-th graph entropy based on degrees of H is defined as Id^t(Η)=-n∑i=1(di^t/∑j=1^ndj^t^nlogdi^t/∑j=1^ndj^t^n)=log(n∑i=1di^t)-n∑i=1(di^t/∑j=1^ndj^tlogdi^t), where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of Id^t(Η) for t = 1, when Η is among all uniform super trees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.
基金Supported by NSFC(Grant Nos.11271300 and 11571135)the project NEXLIZ–CZ.1.07/2.3.00/30.0038+1 种基金the project P202/12/G061 of the Czech Science Foundation and by the European Regional Development Fund(ERDF)the project NTIS-New Technologies for Information Society,European Centre of Excellence,CZ.1.05/1.1.00/02.0090
文摘A graph is called claw-free if it contains no induced subgrapn lsomorpmc to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least ([V(G)I - 2)/3. At the workshop CSzC (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z1 (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if eachend-vertex of every induced copy of H in G has degree at least IV(G)I/3 + 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.end-vertex of every induced copy of H in G has degree at least IV(G)I/3 + 1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.
文摘In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, we derive a result which strengthens substantially the well- known theorem on set systems with k-wise E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 (2004)]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.
基金Supported by NSFC(Grant No.11271300)the Natural Science Foundation of Shaanxi Province(Grant No.2016JQ1002)the Project NEXLIZ–CZ.1.07/2.3.00/30.0038
文摘Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamil- tonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.
基金Supported by National Natural Science Foundation of China(Grant Nos.11871397,12071370 and U1803263)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2020JM-083)。
文摘Let G be a bridgeless graph and C be a circuit in G.To find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp(f)∩E(C)|>3/4|E(C)|,and showed that the conjecture holds if|E(C)|≤19[Combinatorica,37,1097–1112(2017)].In this paper,we prove that the conjecture holds if|E(C)|≤27.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11601431,11871398,12071370,U1803263 and 12131013)the Natural Science Foundation of Shaanxi Province(Grant No.2020JM-099)the Natural Science Foundation of Qinghai Province(Grant No.2020-ZJ-920)。
文摘In this paper,we give some sufficient conditions for extended neighborhood coronas to have Laplacian perfect state transfer.We also give some conditions for extended neighborhood coronas to be periodic.
文摘In this paper, we discuss the connection between the rigid graded selfduality over some noncommutative graded ring and the selfduality over its initial subring.