共查询到16条相似文献,搜索用时 437 毫秒
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设G是一个简单的无向图,若G不是完全图,G的孤立韧度定义为I(G)=min{|s|/i(G-S):S∈V(G),i(G-S)≥2);否则令I(G)=∞.对与图的孤立韧度I(G)密切相关的新参数,I’(G),若G不是完全图,定义I’(G)=min{|s|/i(G-S)-1:S∈V(G),i(G-S)≥2};否则I’(G)=∞本文研究了新参数I‘(G)与图的分数κ-因子的关系,给出了具有某些约束条件的图的分数κ-因子存在的一些充分条件. 相似文献
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图的分数因子与孤立韧度 总被引:3,自引:0,他引:3
图G的孤立韧度定义为I(G)=min{|S|/i(G-S)∶SV(G),i(G-S)≥2},若G不是完全图.否则令I(G)=∞.本文给出了图的分数k因子与图的分数[a,b]因子的存在性与图的孤立韧度的关系.证明了,若δ(G)≥k且I(G)≥k,则G有分数k因子;若δ(G)≥I(G)≥a-1 a/b,则图G有分数[a,b]因子,其中a相似文献
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图的韧度与分数k-因子的存在性 总被引:1,自引:0,他引:1
周思中 《数学的实践与认识》2006,36(6):255-260
设G是一个简单无向图,若G不是完全图,G的韧度的一个变形定义为τ(G)=m in{S/(ω(G-S)-1)∶S V(G),ω(G-S)2}.否则,令τ(G)=∞.本文研究了参数τ(G)与分数k-因子的关系,给出了具有某些约束条件的图的分数k-因子存在的一些充分条件,并提出进一步可研究的问题. 相似文献
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关于图的孤立韧度与分数因子存在性的若干结果 总被引:3,自引:0,他引:3
本文讨论了图的孤立韧度I(G)以及与之相关的参数I^1(G)与图的分数因子存在性的关系,给出了I(G)及I^1(G)与图的分数点(边)消去性、分数L-可扩性及分数[1,b]-因子存在性之间关系的一系列结果. 相似文献
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令G=(V(G),E(G))是一个图,并令9和f是两个定义在V(G)上的整数值函数且对所有的x∈V(G)有g(x)≤f(z)成立.若对G的每一条边e都存在G的一个分数(g,f)-因子G_h使得h(e)=0,其中h是G_h的示性函数,则称G是一个分数(g,f)-消去图,若在G中删去E′■E(G),|E′|=k后,所得图有分数完美匹配,则称G是分数k-边-可消去的。本文给出了图是1-可消去,2-可消去和k-边-可消去的与韧度和孤立韧度相关的充分条件。证明了这些结果在一定意义上是最好可能的. 相似文献
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WU ZeFang LIU GuiZhen & YU QingLin Center for Combinatorics LPMC-TJKLC Nankai University Tianjin China School of Mathematics Sh ong University Jinan 《中国科学 数学(英文版)》2011,(7)
In this paper, we investigate the existence of [a,b]-factors with inclusion/exclusion properties under the toughness condition. We prove that if an incomplete graph G satisfies t(G) (a-1) + ab and a,b are two integers with b > a > 1, then for any two given edges e1 and e2, there exist an [a,b]-factor including e1,e2; and an [a,b]-factor including e1 and excluding e2; as well as an [a,b]-factor excluding e1,e2 unless e1 and e2 have a common end in the case of a = 2. For complete graphs, we obtain a similar r... 相似文献
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Qiuju Bian 《Journal of Applied Mathematics and Computing》2006,22(3):299-304
Let G be a bipartite graph andg and f be two positive integer-valued functions defined on vertex setV(G) ofG such thatg(x) ≤ f(x) for anyx ? V(G). In this paper, a new isolated toughness ofG is defined and some sufficient conditions related to the new toughness forG to have (g,f )-factors are obtained. Furthermore, these results are proved to be sharp in some sense. 相似文献
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Recently Alon and Friedland have shown that graphs which are the union of complete regular bipartite graphs have the maximum number of 1-factors over all graphs with the same degree sequence. We identify two families of graphs that have the maximum number of 1-factors over all graphs with the same number of vertices and edges: the almost regular graphs which are unions of complete regular bipartite graphs, and complete graphs with a matching removed. The first family is determined using the Alon and Friedland bound. For the second family, we show that a graph transformation which is known to increase network reliability also increases the number of 1-factors. In fact, more is true: this graph transformation increases the number of k-factors for all k≥1, and “in reverse” also shows that in general, threshold graphs have the fewest k-factors. We are then able to determine precisely which threshold graphs have the fewest 1-factors. We conjecture that the same graphs have the fewest k-factors for all k≥2 as well. 相似文献
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