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第一类图的一个充分条件
  • ISSN号：0254-3079
  • 期刊名称：《应用数学学报》
  • 时间：0
  • 分类：O157.5[理学—数学;理学—基础数学]
  • 作者机构：[1]浙江师范大学数理与信息工程学院,金华321004
  • 相关基金：国家自然科学基金（10771197）资助项目.
作者： 陈永珠[1], 王维凡[1]
关键词： 图, 圈, 边染色, 欧拉示性数, graph, cycle, edge coloring, Euler characteristic
中文摘要：

图G的一个k-边染色是一个映射φ：E（G）→{1,2,…k）,使得每一对相邻边x和y,有φ（x）≠φ（y）.G的边色数x′（G）是使得G有一个k-边染色的最小的整数k.本文证明了：如果G是一个最大度为6能嵌入到欧拉示性数非负的曲面的图,且满足下列条件之一,那么x′（G）=6：（1）不含带弦4-圈;（2）同时不含带弦5-圈和带弦6-圈.

英文摘要：

A k-edge coloring of a graph G is a mapping φ from E（G） to the color set （1, 2,..., k） such that any two adjacent edges have different colors. The chromatic index X＇（G） is the smallest integer k such that G admits a k-edge coloring. In this paper, we prove that every graph G with maximum degree 6 which is embeddable in a surface of nonegative Euler characteristic has X＇（G） = 6 if either G has no 4-cycle with a chord, or G has no 5- and 6-cycle with a chord.

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期刊信息
  • 《应用数学学报》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国数学会 中国科学院数学与系统科学研究院
  • 主编：丁夏畦
  • 地址：北京市海淀区中关村东路55号
  • 邮编：100190
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：0254-3079
  • 国内统一刊号：ISSN：11-2040/O1
  • 邮发代号:2-822
  • 获奖情况:
  • 1996、2000年获“中科院优秀科技期刊”三等奖,1997年获“第二届全国优秀科技期刊”三等奖,2001年入选“双效期刊”（中国期刊方阵）
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:6864