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本文研究了复合图1-因子分解问题,给出了复合图可1-因子分解的几个充分条件.设图G和H都是正则因,那么G和H的复合图G[H]可1-因子分解,如果G和H满足下列三个条件之一:(1)G可1-因子分解;(2)G至少有 1-因子,H为偶阶正则图[V(H)|≥2;(3)G可以分解为一些1-因子和2-因子之并,H为偶阶正则图且至少有max{0,△(H)-4}个1-因子. 相似文献
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图$G$的正常边染色称为无圈的, 如果图$G$中不含2-色圈, 图$G$的无圈边色数用$a''(G)$表示, 是使图$G$存在正常无圈边染色所需要的最少颜色数. Alon等人猜想: 对简单图$G$, 有$a''(G)\leq{\Delta(G)+2}$. 设图$G$是围长为$g(G)$的平面图, 本文证明了: 如果$g(G)\geq3$, 则$a''(G)\leq\max\{2\Delta(G)-2,\Delta(G)+22\}$; 如果 $g(G)\geq5$, 则$a''(G)\leq{\Delta(G)+2}$; 如果$g(G)\geq7$, 则$a''(G)\leq{\Delta(G)+1}$; 如果$g(G)\geq16$并且$\Delta(G)\geq3$, 则$a''(G)=\Delta(G)$; 对系列平行图$G$, 有$a''(G)\leq{\Delta(G)+1}$. 相似文献
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一个平面图G的边面色数xef(G)是指对G的边和面进行染色所用最少的颜色数目,并同时使得相邻或相关联的两个元素间染不同颜色.若G是一个系列平行图,也就是不含K_4的剖分作为子图的平面图,则有Xef(G)≤max{7,△(G) 1};同时如果G还是2-连通的且△(G)>6,则有Xef(G)=△. 相似文献
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On the Coloring of Series-Parallel Graphs 总被引:1,自引:0,他引:1
Throughoutthispaper,allgraphsarefinite,simpleandundirected.ForagraphG,weuseV(G),E(G),(G)and(G)todenotethevertexset,theedgeset,themaximum(vertex)degreeandtheminimum(vertex)degreeofG.IfvV(G),NG(v)denotesthesetofverticesarjacenttov,thedegreedG(v)is|NG(v... 相似文献
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A ubiquitous phenomenon in networks is the presence of communities within which the network connections are dense and between which they are sparser.This paper proposes a max-flow algorithm in bipartite networks to detect communities in general networks.Firstly,we construct a bipartite network in accordance with a general network and derive a revised max-flow problem in order to uncover the community structure.Then we present a local heuristic algorithm to find the optimal solution of the revised max-flow problem.This method is applied to a variety of real-world and artificial complex networks,and the partition results confirm its effectiveness and accuracy. 相似文献
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食管黏膜下隆起性病变是胃镜检查时较常见的病变,可为食管黏膜和黏膜下肿物及消化道壁外组织脏器等压迫所致的隆起,由于病变表面覆盖正常黏膜上皮,常规胃镜无法准确判断其层次来源、性质和大小。纵轴超声内镜(endoscopic ultrasonography,EUS)能在胃腔内对隆起性病变进行超声扫描,了解其结构、大小及来源,并根据超声内镜检查结果确定进一步治疗方案。笔者回顾了在本院及外院检查发现食管黏膜下隆起性病变、在本院行纵轴EUS检查的34例患者,分析纵轴EUS检查在食管隆起性病变中的诊断及鉴别的价值。 相似文献