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
针对车-车(vehicle to rechicle,V2V)通信系统对无线电信道衰落特性和模型的需求,分别在两种隧道场景中5.9 GHz和5.2 GHz频段下进行了V2V无线电信道测量活动,并对隧道外、隧道内和两者之间的连接部分场景进行了小尺度衰落特性分析.基于...针对车-车(vehicle to rechicle,V2V)通信系统对无线电信道衰落特性和模型的需求,分别在两种隧道场景中5.9 GHz和5.2 GHz频段下进行了V2V无线电信道测量活动,并对隧道外、隧道内和两者之间的连接部分场景进行了小尺度衰落特性分析.基于近距离(close-in,CI)对数模型和ABG(α-β-γ)模型建立了基于距离的接收功率模型,对两种场景隧道内外的接收功率进行了评估和比较,路径损耗指数分别为1.83和1.9,结果表明参考距离为1 m的CI对数模型具有更高的拟合度.此外,将测量数据幅度的衰落分布与五种典型的理论衰落分布进行比较分析,发现其特征更接近于具有最小拟合优度值的莱斯分布,且隧道内的莱斯K因子小于隧道外.同时,给出了隧道内和隧道外之间连接处基于距离的莱斯K因子模型,发现连接处的K因子与距离无关,而隧道内的K因子随距离增大而减小.展开更多
In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime numbe...In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.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
A graph G is called a (g, f)-uniform graph if for each edge of G, there is a(g, f)-factor containing it and another (g, f)-factor excluding it. In this paper a necessary andsufficient condition for a graph to be a (g,...A graph G is called a (g, f)-uniform graph if for each edge of G, there is a(g, f)-factor containing it and another (g, f)-factor excluding it. In this paper a necessary andsufficient condition for a graph to be a (g, f)-uniform graph is given and some applications of thiscondition are discussed. In particular, some simple sufficient conditions for a graph to be an [a,b]-uniform graph are obtained for a b.展开更多
The nomograph by Wischmeier et al.(1971)for calculating the K-factor in the USLE was extremely useful when there was low access to calculators.However,the generalised calculation of this factor requires the developmen...The nomograph by Wischmeier et al.(1971)for calculating the K-factor in the USLE was extremely useful when there was low access to calculators.However,the generalised calculation of this factor requires the development of analytic procedures.This paper presents a detailed analysis of the nomograph and its underlying equation,which is applicable only when the silt plus very find sand fraction does not exceed 70%.We also examined the quality of fit on the nomograph of the adaptations to the equation that have been proposed,as a means of dealing with those areas where the original equation is not applicable.All models are shown to have areas where the fit is deficient or even unacceptable.Besides,the family of curves on the nomograph for the various values taken by the organic matter are not coincident with the mathematical function from which they presumably derive.The study also identifies those areas of the textural triangle in which the soils originally used in developing the USLE are located,with a view to according a lower predictive value to the contrasting areas in which calculations of the K-factor will necessarily be extrapolations.Finally,a new equation for calculating the K-factor is presented,which accurately reproduces the different sections of the nomograph,and allows the poorly functioning graph to be dispensed with.The paper ends with a link to a tool in R for simplifying the procedure for calculating the K-factor,taking into account varying situations of data availability.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In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.
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 National Natural Science Foundation (10471078, 10201019) and RSDP (20040422004) of China
文摘A graph G is called a (g, f)-uniform graph if for each edge of G, there is a(g, f)-factor containing it and another (g, f)-factor excluding it. In this paper a necessary andsufficient condition for a graph to be a (g, f)-uniform graph is given and some applications of thiscondition are discussed. In particular, some simple sufficient conditions for a graph to be an [a,b]-uniform graph are obtained for a b.
文摘The nomograph by Wischmeier et al.(1971)for calculating the K-factor in the USLE was extremely useful when there was low access to calculators.However,the generalised calculation of this factor requires the development of analytic procedures.This paper presents a detailed analysis of the nomograph and its underlying equation,which is applicable only when the silt plus very find sand fraction does not exceed 70%.We also examined the quality of fit on the nomograph of the adaptations to the equation that have been proposed,as a means of dealing with those areas where the original equation is not applicable.All models are shown to have areas where the fit is deficient or even unacceptable.Besides,the family of curves on the nomograph for the various values taken by the organic matter are not coincident with the mathematical function from which they presumably derive.The study also identifies those areas of the textural triangle in which the soils originally used in developing the USLE are located,with a view to according a lower predictive value to the contrasting areas in which calculations of the K-factor will necessarily be extrapolations.Finally,a new equation for calculating the K-factor is presented,which accurately reproduces the different sections of the nomograph,and allows the poorly functioning graph to be dispensed with.The paper ends with a link to a tool in R for simplifying the procedure for calculating the K-factor,taking into account varying situations of data availability.
