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高度图的独立集复形   总被引:3,自引:0,他引:3  
给定图G,称以G的所有独立集为单形的抽象复形I(G)为G的独立集复形.如果两个图G和H的独立集复形I(G)和I(H)的各阶同调群都是同构的,则称两个图是独立同调的.J(G)表示Gc的连通分支数,J3K2(G)表示Gc中同构于(3H2)c的连通分支数.本文研究了最小次δ(G)至少为其阶数|V(G)|减5的图G的独立集复形的结构,对满足δ(G)≥|V(C)|5,δ(H)≥|V(H)|-5的两个图G和H,(I)证明了,G和H独立同调的充要条件为J(G)=J(H),J3K2(G)=J3K2(H),且I(G)和I(H)的Euler示性数相同.(Ⅱ)给出了一个在图上计算I(G)的一维Betti数的方法,得到了一个I(G)是无圈复形的充要条件  相似文献
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ON 3-CHOOSABILITY OF PLANE GRAPHS WITHOUT 6-,7- AND 9-CYCLES   总被引:2,自引:0,他引:2  
The choice number of a graph G,denoted by X1(G),is the minimum number k such that if a list of k colors is given to each vertex of G,there is a vertex coloring of G where each vertex receives a color from its own list no matter what the lists are. In this paper,it is showed that X1 (G)≤3 for each plane graph of girth not less than 4 which contains no 6-, 7- and 9-cycles.  相似文献
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Let I with |I| = k be a matching of a graph G (briefly, I is called a k-matching). If I is not a proper subset of any other matching of G, then I is a maximal k-matching and m(gk, G) is used to denote the number of maximal k-matchings of G. Let gk be a k-matching of G, if there exists a subset {e1, e2,…, ei} of E(G) \ gk, i (?)1, such that (1) for any j ∈ {1, 2,…,i}, gk + {ej} is a (k + l)-matching of G; (2) for any f ∈ E(G) \ (gk ∪ {e1,e2,…,ei}), gk + {f} is not a matching of G; then gk, is called an i wings k-matching of G and mi(gk,G) is used to denote the number of i wings k-matchings of G. In this paper, it is proved that both mi(gk,G) and m(gk,G) are edge reconstructible for every connected graph G, and as a corollary, it is shown that the matching polynomial is edge reconstructible.  相似文献
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本文证明了图与其去点主子图的独立集复形构成的相对同调群族是可重构的;当图满足一定的条件时,图与其去点主子图的邻域复形构成的相对同调群族也是可重构的.  相似文献
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ONTHETOTALCOLORINGOFGRAPHG∨H¥XuBaogang(许宝刚)(Math.ofDept.,ShandongUniversity,Jinan250100,China.)Abstract:Thetotalchromaticnumb...  相似文献
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一个图G的全色数χT(G)是使得V(G)∪E(G)中相邻或相关联元素均染不同颜色的最少颜色数.文中证明了,若图G只有唯一的一个4度最大度点,则χT(G)=Δ(G)+1.  相似文献
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Let G is a simple graph,ω(G).△(G)、x(G)are maximum clique number ofG,maximum degree and chromatic number of G respectively.In[2],James defi-nes that(a,b,c)(where a,b,c are positive integer)is graphical if there existsG whichω(G)=a,x(G)=b,△(G)=c.We say G is on(a,b,c)and set P(a,b,(a,b,c)=min{|V(G)||G is on(a,b,c)}.All other signs are from[1].  相似文献
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Let G be a graph, let s be a positive integer, and let X be a subset of V(G). Denote δ(X) to be the minimum degree of the subgraph G[X] induced by X. A partition(X, Y) of V(G) is called s-good if min{δ(X), δ(Y)} s. In this paper, we strengthen a result of Maurer and a result of Arkin and Hassin, and prove that for any positive integer k with 2 k |V(G)|- 2, every connected graph G with δ(G) 2 admits a1-good partition(X, Y) such that |X| = k and |Y| = |V(G)|- k, and δ(X) + δ(Y) δ(G)- 1.  相似文献
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