Coloring (gem, co‐gem)‐free graphs |
| |
Abstract: | A gem is a graph that consists of a path on four vertices plus a vertex adjacent to all four vertices of the path. A co‐gem is the complement of a gem. We prove that every (gem, co‐gem)‐free graph G satisfies the inequality (a special case of a conjecture of Gyárfás) and the inequality (a special case of a conjecture of Reed). Moreover, we give an ‐time algorithm that computes the chromatic number of any (gem, co‐gem)‐free graph with n vertices, while the existing algorithm in the literature takes . |
| |
Keywords: | χ ‐boundedness chromatic number clique size degree |
|
|