Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647628 | Discrete Mathematics | 2013 | 5 Pages |
Abstract
A graph G is called improperly (d1,d2,â¦,dk)-colorable, or simply (d1,d2,â¦,dk)-colorable, if the vertex set of G can be partitioned into subsets V1,V2,â¦,Vk such that the graph G[Vi] induced by Vi has maximum degree at most di for 1â¤iâ¤k. In 1976, Steinberg raised the following conjecture: every planar graph without 4- and 5-cycles is (0,0,0)-colorable. Up to now, this challenge conjecture is still open. In this paper, we prove that every planar graph without cycles of length 4 and 6 is (1,1,0)-colorable.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yuehua Bu, Caixia Fu,