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binding number and Fractional k-Factors of Graphs

Journal of Applied Mathematics and Physics 2024年第7期12卷 2594-2600页

作者： Renying Chang Business School Shanghai Dianji University Shanghai China

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.

关键词： binding number Fractional k-Factor Fractional Matching Independent Set Covering Set

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ON THE EDGE-binding number OF SOME PLANE GRAPHS

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Acta Mathematicae Applicatae Sinica 2001年第4期17卷 443-448页

作者：刘林忠张忠辅王建方 Department of Management Engineering Lanzhou Railway Institute Lanzhou China Institute of Applied Mathematics Lanzhou Railway Institute Lanzhou China Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Let G(V,E) be a simple graph, the edge-binding number b1 (G) of G is defined as where N(S) denotes the adjacent edges set of S. In this paper, we obtained the edge-binding number of outer plane graphs, Halin graph and... 详细信息

关键词： Graph binding number edge-binding number

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Some Existence Theorems on Path Factors with Given Properties in Graphs

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Acta Mathematica Sinica,English Series 2020年第8期36卷 917-928页

作者： Si Zhong ZHOU Zhi Ren SUN School of Science Jiangsu University of Science and TechnologyZhenjiang 212003P.R.China School of Mathematical Sciences Nanjing Normal UniversityNanjing 210046P.R.China

A path factor of G is a spanning subgraph of G such that its each component is a path.A path factor is called a P≥n-factor if its each component admits at least n vertices.A graph G is called P≥n-factor covered if G admits a P≥n-factor containing e for any e∈E(G),which is defined by[Discrete Mathematics,309,2067-2076(2009)].We first define the concept of a(P≥n,k)-factor-critical covered graph,namely,a graph G is called(P≥n,k)-factor-critical covered if G-D is P≥n-factor covered for any D⊆V(G)with|D|=*** this paper,we verify that(i)a graph G withκ(G)≥k+1 is(P≥2,k)-factor-critical covered if bind(G)>2+k/3;(ii)a graph G with|V(G)|≥k+3 andκ(G)≥k+1 is(P≥3,k)-factor-critical covered if bind(G)≥4+k/3.

关键词： Graph binding number P≥2-factor P≥3-factor (P≥2,k)-factor-critical covered graph (P≥3,k)-factor-critical covered graph

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Remarks on Component Factors

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Journal of the Operations Research Society of China 2023年第3期11卷 657-666页

作者： Wei Gao Wei-Fan Wang School of Information Science and Technology Yunnan Normal UniversityKunming650500YunnanChina Department of Mathematics Zhejiang Normal UniversityJinhua321004ZhejiangChina

In this remark,we first simply survey the important results on component factors in ***,we focus on the binding number condition of component factors in some special *** main contributions in this remark are two folded:(1)we reveal that the existence of some special component factors is equal to some specific binding number conditions;(2)the parameter conditions for a graph G with a P≥3-factor are determined.

关键词： H-factor Component factor binding number

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