| 刘林忠,张忠辅,王建方.最大度不小于5的外平面图的邻强边染色(英文)[J].数学研究及应用,2005,25(2):255~266 |
| 最大度不小于5的外平面图的邻强边染色(英文) |
| On the Adjacent Strong Edge Coloring of Outer Plane Graphs |
| 投稿时间：2003-02-09 |
| DOI：10.3770/j.issn:1000-341X.2005.02.007 |
| 中文关键词: 外平面图 点可区分边染色 邻强边染色 |
| 英文关键词:outer plane graph vertex distinguishing edge coloring adjacent strong edge coloring. |
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| 摘要点击次数: 2591 |
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| 中文摘要: |
| 图G(V,E)的一k-正常边染色叫做k-邻强边染色当且仅当对任意uv∈E(G)有,f[u]≠f[v],其中f[u]={f(uw)|uw∈E(G)},f(uw)表示边uw的染色.并且x′as(G)=min{k|存在k-图G的邻强边染色}叫做图G的图的邻强边色数.本文证明了对最大度不小于5的外平面图有△≤x′as(G)≤△+1,且x′as(G)=△+1当且仅当存在相邻的最大度点. |
| 英文摘要: |
| A k-adjacent strong edge coloring of graph G(V, E) is defined as a proper kedge coloring f of graph G(V, E) such that f[u] ≠ f[v] for every uv ∈ E(G), where f[u] ={f(uw)|uw ∈ E(G)} and f(uw) denotes the color of uw, and the adjacent strong edge chromatic number is defined as x′as(G) = min{k| there is a k-adjacent strong edge coloring of G}. In this paper, it has been proved that △≤ x′as(G) ≤△ + 1 for outer plane graphs with △(G) ≥ 5, and x′as(G) = △ + 1 if and only if there exist adjacent vertices with maximum degree. |
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