共查询到17条相似文献,搜索用时 78 毫秒
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利用伴随多项式来讨论图的着色唯一性是近二十年来出现的新方法.用Pn表示有n个顶点的路.Dn表示把K3的一个顶点与Pn-2的一个一度顶点重迭后得到的图.该文推广了相关文献的结论,得到D^-n色唯一当且仅当n≠4且n≠8.彻底解决了这类图的色性. 相似文献
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讨论了形如kCRUrPR的一类图的补图的色性.在一定的条件下证明了这类图是色唯一的.本文推广了文[1]的结果. 相似文献
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张树生 《数学的实践与认识》2001,31(6):675-679
本文证明了 :如果对每个 i∈ {1 ,2 ,… ,t},都有 ni≥ 5 ,且 ni是正整数 ,那么 Cn1∪ Cn2 ∪…∪ Cnt是色唯一的 相似文献
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一类K_n-E(G)型图的色唯一性 总被引:2,自引:0,他引:2
设Km-E(G)表示从完全图Km中删去一个和G同构的子图的所有边而得到的图.本文证明了,当G=k1Ps1∪k2PS2∪…∪krPsr,(si>1,si≠4,i=1,2,…,r),且Psi都是不可约路时,图Km-E(G)是色唯一的. 相似文献
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圈和Dn图的补图的色唯一性 总被引:37,自引:0,他引:37
圈和Dn图的补图的色唯一性王守中刘儒英(青海师范大学数学系,西宁810008)关键词图,色多项式,色唯一性.分类号AMS(1991)05C/CCLO157.5用Pn和Cn表示有n个顶点的路和圈.用Dn表示把K3的一个顶点与Pn-2的一个一度顶点重迭后... 相似文献
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张秉儒 《纯粹数学与应用数学》1997,13(1):61-67
记δn=Σ↓k≤n(^kn-k),在本文中证明了:A↓r∈N,若A↓∈N,若A↓∈{1,2,…,r},qi(〉5)都是素数,并且[(δqi-1-1)!+1]/δqi-1是正整数,则图簇Kn-E(k0P3∪k1Pq1-1∪…∪krPqr-1)是色唯一的,推广了文[1]的结果。 相似文献
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The Chromaticity of Certain Complete Multipartite Graphs 总被引:4,自引:0,他引:4
In this paper, we first establish a useful inequality on the minimum real roots of the adjoint polynomials of the complete graphs. By using it, we investigate the chromatic uniqueness of certain complete multipartite graphs. An unsolved problem (i.e., Problem 11), posed by Koh and Teo in Graph and Combin. 6(1990) 259–285, is completely solved by giving it a positive answer. Moreover, many existing results on the chromatic uniqueness of complete multipartite graphs are generalized.Acknowledgments. The authors are greatly indebted to the referees for their valuable comments and suggestions, which are very helpful for improving the presentation of the paper. The work is supported by National Science Foundation of China and the Science Foundation of the State Education Ministry of China.Final version received: January 9, 2004AMS Subject Classification (2000): 05C15, 05C60 相似文献
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引入伴随多项式是为了从补图的角度研究色多形式,图的伴随多项式的极小根可用于判定色等价图.β(G)表示图G的伴随多项式的极小根.n表示n个顶点的单圈图的集合.分别确定了具有max{β(G)|G∈Ωn}和min{β(G)|G∈Ωn}的所有单圈图. 相似文献
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Let P(G,λ) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H,λ)=P(G,λ) implies H is isomorphic to G. For integers k≥0, t≥2, denote by K((t−1)×p,p+k) the complete t-partite graph that has t−1 partite sets of size p and one partite set of size p+k. Let K(s,t,p,k) be the set of graphs obtained from K((t−1)×p,p+k) by adding a set S of s edges to the partite set of size p+k such that 〈S〉 is bipartite. If s=1, denote the only graph in K(s,t,p,k) by K+((t−1)×p,p+k). In this paper, we shall prove that for k=0,1 and p+k≥s+2, each graph G∈K(s,t,p,k) is chromatically unique if and only if 〈S〉 is a chromatically unique graph that has no cut-vertex. As a direct consequence, the graph K+((t−1)×p,p+k) is chromatically unique for k=0,1 and p+k≥3. 相似文献
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For a graph G, let P(G) be its chromatic polynomial. Two graphs G and H are chromatically equivalent if P(G)=P(H). A graph G is chromatically unique if P(H)=P(G) implies that H≅G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2∪Pm(m?3), (K2,2,2-e)∪Pm(m?5) and (K2,2,2-2e)∪Pm(m?6) by identifying the end-vertices of the path Pm with any two vertices of K2,2,2, K2,2,2-e and K2,2,2-2e, respectively, where e and 2e are, respectively, an edge and any two edges of K2,2,2. As a by-product of this, we obtain some families of chromatically unique and chromatically equivalent classes of graphs. 相似文献
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通过研究SGS*类图簇的伴随多项式的因式分解,证明了这类图簇的补图的色等价图的结构特征. 相似文献
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关于K4同胚图色唯一性的几个新结果 总被引:4,自引:0,他引:4
本文证得:如果i,j,k,l,m,n中有四个数相等,而另外二个数不小于此数,则K_4(i,j,k,l,m,n)是色唯一的.此外,我们还得到了另外两族具有色唯一性的K_4同胚图. 相似文献