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1-树图的邻强边染色 被引量:10

On The Adjacent Strong Edge Coloring of 1-Tree
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摘要 图G的-k-正常边染色f若使得任意uv∈E(G)满足f「u」≠「v」,其中f「u」=「f(uw|uw∈E(G)」,则称f为G的-k-邻强边染色,简称K-ASEC,并称Xaf(G)=min(K|存在C的-k-ASEC「为G的邻强边色数,本文提出了邻强边染色猜地2连通图G(V,E)≠C5),有△(G)≤Xas(G)01600187(G)+2,并研究了1-树图的邻强边染色。 Let G(V,E) be a graph. A k -proper edge coloring f is called a k -adjacent strong edge coloring of G(V,E) iff every uv∈ E(G) satisfies f[u] ≠ f[v], where f[u] = (f(uw) |uw∈E(G) }, is called k -ASEC for short, and X_(as)~'(G) = min{k | There exists a k-ASEC of G} is called the adjacent strong edge chromatic number of G. In this paper,we present a conjec- ture that for 2-connected graph G(V,E) (G(V,E) ≠ C_5 ),△ (G) ≤X_(as)~'(G) ≤ △(G) + 2, and prove that for 1-tree graph with△(G)≥4 have△(G) ≤ X_(as)~'(G) ≤ △(G) + 1 and X_(as)~'(G)= △(G) + 1 iff E(G[V_△]) ≠( , where V_△= {u|u∈ V(G), d(u) =△(G)}.
出处 《Journal of Mathematical Research and Exposition》 CSCD 2000年第2期299-305,共7页 数学研究与评论(英文版)
基金 国家自然科学基金!19871036
关键词 邻强边染色 邻强边色数 1-树图 K-ASEC 连通图 graph adjacent strong edge coloring adjacent strong edge chromatic number.
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参考文献1

  • 1BURNS A C,SCHELP R H.Vartex-distinguishing proper edge-colorings[].Journal of Graph Theory.1997

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