Validity of Borodin & Kostochka Conjecture for a Class of Graphs
arXiv:1705.03195
Abstract
Borodin & Kostochka conjectured that if maximum degree of a graph is greater than or equal to 9, then the chromatic number of the graph is less than or equal to maximum of ω and maximum degree minus 1. Here we prove that this Conjecture is true for {P3 UNION K1}-free graphs and {K2 UNION complement of K2}-free graphs.
3 pages