马德,刘林忠,张忠辅.1-树图的邻强边染色[J].数学研究及应用,2000,20(2):299~305 |
1-树图的邻强边染色 |
On The Adjacent Strong Edge Coloring of 1-Tree |
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DOI:10.3770/j.issn:1000-341X.2000.02.031 |
中文关键词: 图 邻强边染色 邻强边色数. |
英文关键词:graph adjacent strong edge coloring adjacent strong edge chromatic number. |
基金项目:国家自然科学基金资助课题(19871036) |
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中文摘要: |
图G的一k-正常边染色f若使得任意uv∈E(G)满足f[u]≠f[v],其中f[u]={f(uω)|uw∈E(G)},则称f为G的一k-邻强边染色,简称k-ASEC,并称χas(G)=min{k|存在G的一k-ASEC}为G的邻强边色数.本文提出了邻强边染色猜想:对2-连通图G(V,E)(G(V,E)≠C5),有△(G)≤χas(G)≤△(G)+2,并研究了1-树图的邻强边染色,证明了对△(G)≥4的1-树图G有△(G)≤χas< |
英文摘要: |
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 χas(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) ≠ C5),△ (G) ≤χas(G) ≤ △(G) + 2, and prove that for 1-tree graph with △(G)≥4 have △(G) ≤ χas(G) ≤ △(G)+1 and χas(G) = △(G)+1 iff E(G[V△])≠φ,where V△=(u|u∈V(G),d(u)=△(G)}. |
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