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On adjacent-vertex-distinguishing total coloring of graphs   总被引:40,自引:0,他引:40  
In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number of some graphs such as cycle, complete graph, complete bipartite graph, fan, wheel and tree.  相似文献
2.
ON THE COMPLETE CHROMATIC NUMBER OF HALIN GRAPHS   总被引:8,自引:0,他引:8  
ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.Write.1.IntroductionDefinition1.FOrany3-connectedplanargraphG(V,E,F)withA(G)23,iftheboundaryedgesoffacefowhichisadjacenttotheothersareremoved,itbecomesatree,andthedegreeofeachvertexofV(fo)is3,andthenGiscalledaHalingraph;foiscalledtheouterfaceofG,andtheotherscalledtheinteriorfaces,thevenicesonthefacefoarecalledtheoutervenices,theoillersarecalledtheinterior...ti..,tll.ForanyplanargraphG(V,E,F),f,f'eF,fisadjacenttof'ifan…  相似文献
3.
3-正则Halin-图全色数的注(英文)   总被引:4,自引:0,他引:4  
本文讨论了△(G)=3的Halin-图的金色数Xr(G)=4的充分条件,并提出了3-正则Halin-图Xr(G)=5的充分必要条件的猜想,其中△(G),Xr(G)分别表示G的最大度和全色数.  相似文献
4.
A total cover of a graph G is a subset of V(G)E(G) which covers all elements of V(G)E(G). The total covering number 2(G) of a graph G is the minimum cardinality of a total cover in G. In [1], it is proven that 2(G)[n/2] for a connected graph G of order n. Here we consider the extremal case and give some properties of connected graphs which have a total covering number [n/2]. We prove that such a graph with even order has a 1-factor and such a graph with odd order is factor-critical.  相似文献
5.
It is conjectured that χas(G) = χt(G) for every k-regular graph G with no C5 component (k 2). This conjecture is shown to be true for many classes of graphs, including: graphs of type 1; 2-regular, 3-regular and (|V (G)| - 2)-regular graphs; bipartite graphs; balanced complete multipartite graphs; k-cubes; and joins of two matchings or cycles.  相似文献
6.
In this paper, some properties of Ramsey numbers are studied, and the following results are presented.
1. (1) For any positive integers k1, k2, …, km l1, l2, …, lm (m> 1), we have
.
2. (2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have
. Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties.
  相似文献
7.
BOUNDSONTHELOWERSIZEOFA7-CRITICALGRAPHLIUHUANPING(刘焕平)(DepartmentofMathematics,HarbinNormalUniversity,Harbin150080,China)ZHAN...  相似文献
8.
A short proof of Nash-Williams' Theorem on the arboricity of a graph is given.  相似文献
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