In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This stud...The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This study was carried out over the city of Lokoja,Nigeria,using ten years(2011 to 2020)atmospheric data of temperature,pressure and humidity both at the surface(12 m)and at 100 m AGL.The data were retrieved from European Centre for Medium-Range Weather Forecasts(ECMWF)ERA5.The k-factor yearly variation follows the same trend with minimum and maximum values obtained during dry and wet season months respectively.In addition,the highest mean value of 1.00042 was recorded in the month of August while the lowest value of 1.00040 was recorded in the month of January with an overall mean value of 1.0003.This value is less than the recommended standard of 1.33 by ITU-R.The propagation effect corresponding to k<1.33 is sub-refractive.The implication of this on radio wave propagation,especially terrestrial communications is that transmitted wireless signal is prone to losses.This can be mitigated through an effective power budget:Choice of transmitting antenna’s height and gain,so as to improve the Quality of Service over the study area.展开更多
Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that...Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.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
Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I o...Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.展开更多
Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e...Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.展开更多
We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Ja...We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Jachson, respectively.展开更多
Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that...Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.展开更多
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
文摘The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This study was carried out over the city of Lokoja,Nigeria,using ten years(2011 to 2020)atmospheric data of temperature,pressure and humidity both at the surface(12 m)and at 100 m AGL.The data were retrieved from European Centre for Medium-Range Weather Forecasts(ECMWF)ERA5.The k-factor yearly variation follows the same trend with minimum and maximum values obtained during dry and wet season months respectively.In addition,the highest mean value of 1.00042 was recorded in the month of August while the lowest value of 1.00040 was recorded in the month of January with an overall mean value of 1.0003.This value is less than the recommended standard of 1.33 by ITU-R.The propagation effect corresponding to k<1.33 is sub-refractive.The implication of this on radio wave propagation,especially terrestrial communications is that transmitted wireless signal is prone to losses.This can be mitigated through an effective power budget:Choice of transmitting antenna’s height and gain,so as to improve the Quality of Service over the study area.
基金Supported by National Natural Science Foundation of China.
文摘Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.
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.
基金supported by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)+3 种基金333 Project of Jiangsu Provincethe National Social Science Foundation of China(Grant No.14AGL001)the Natural Science Foundation of Xinjiang Province of China(Grant No.2015211A003)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(Grant No.14KJD110002)
文摘Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.
基金sponsored by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)the National Social Science Foundation of China(Grant No.11BGL039)+1 种基金Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Province
文摘Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.
基金supported by the Key Laboratory of Power System,Tsinghua University
文摘We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Jachson, respectively.
基金FRGHong Kong Baptist University NSFC (60673047)SRFDP (20040422004) of China
文摘Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.
