On Parsimonious Edge-Colouring of Graphs with Maximum Degree Three

被引：8
|
作者：
Fouquet, J. -L. [1 ]
Vanherpe, J. -M. [1 ]
机构：
[1] Univ Orleans, Fac Sci, LIFO, F-45067 Orleans 2, France
来源：
GRAPHS AND COMBINATORICS | 2013年 / 29卷 / 03期
关键词：
Cubic graph; Edge-colouring; SUBGRAPHS;
D O I：
10.1007/s00373-012-1145-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a graph G of maximum degree Delta, let gamma denote the largest fraction of edges that can be Delta edge-coloured. Albertson and Haas showed that when G is cubic. We show here that this result can be extended to graphs with maximum degree 3, with the exception of a graph on 5 vertices. Moreover, there are exactly two graphs with maximum degree 3 (one being obviously the Petersen graph) for which This extends a result given by Steffen. These results are obtained by using structural properties of the so called delta-minimum edge colourings for graphs with maximum degree 3.
引用
收藏
页码：475 / 487
页数：13
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