Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647573 | Discrete Mathematics | 2013 | 6 Pages |
Abstract
We study Steinberg's Conjecture. A graph is (c1,c2,â¦,ck)-colorable if the vertex set can be partitioned into k sets V1,V2,â¦,Vk such that for every i with 1â¤iâ¤k the subgraph G[Vi] has maximum degree at most ci. We show that every planar graph without 4- or 5-cycles is (3,0,0)-colorable. This is a relaxation of Steinberg's Conjecture that every planar graph without 4- or 5-cycles is properly 3-colorable (i.e., (0,0,0)-colorable).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Owen Hill, Diana Smith, Yingqian Wang, Lingji Xu, Gexin Yu,