EXTENDING PARTIAL EDGE COLORINGS OF CARTESIAN PRODUCTS OF GRAPHS

被引：0
|
作者：
Casselgren, Carl Johan [1 ]
Petros, Fikre B. [2 ]
Fufa, Samuel A. [2 ]
机构：
[1] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden
[2] Addis Ababa Univ, Dept Math, Addis Ababa 1176, Ethiopia
来源：
DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2024年
基金：
瑞典研究理事会;
关键词：
precoloring extension; edge coloring; Cartesian product; list; bipartite graphs [12]; coloring; PRECOLORING EXTENSION;
D O I：
10.7151/dmgt.2541
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the problem of extending partial edge colorings of Cartesian products of graphs. More specifically, we suggest the following Evans -type conjecture. If G is a graph where every precoloring of at most k precolored edges can be extended to a proper chi 0(G)-edge coloring, then every precoloring of at most k + 1 edges of G ❑K2 is extendable to a proper (chi'(G) + 1)edge coloring of G ❑K2. In this paper we verify that this conjecture holds for trees, complete and complete bipartite graphs, as well as for graphs with small maximum degree. We also prove versions of the conjecture for general regular graphs where the precolored edges are required to be independent.
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页数：25
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