On the Nordhaus-Gaddum problem for 3-defective colorings of P4-free graphs

Abstract

The k-defective chromatic number k(G) of a graph G is the least positive integer
m assigned to the vertices of G such that the maximum degree of the vertex induced subgraph
receiving the same colors is at most k. Madox conjectured that k(G)+k(G) ≤ 2+⌈ p−1
k+1 ⌉ for
any graph of order p. This paper verifies this conjecture for k = 3 and a P4 − free graph.