Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903833 | Journal of Combinatorial Theory, Series B | 2018 | 46 Pages |
Abstract
Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring Ï of a cycle C of G that does not extend to a 3-coloring of G, then G has a subgraph H on O(|C|) vertices that also has no 3-coloring extending Ï. This is asymptotically best possible and improves a previous bound of Thomassen. In the next paper of the series we will use this result and the attendant theory to prove a generalization to graphs on surfaces with several precolored cycles.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
ZdenÄk DvoÅák, Daniel Král', Robin Thomas,