New results on generalized graph coloring [article]

Vladimir E. Alekseev, Alastair Farrugia, Vadim V. Lozin
2003 arXiv   pre-print
For graph classes P_1,...,P_k, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph G can be partitioned into subsets V_1,...,V_k so that V_j induces a graph in the class P_j (j=1,2,...,k). If P_1 = ... = P_k is the class of edgeless graphs, then this problem coincides with the standard vertex k- colorability, which is known to be NP-complete for any k> 3. Recently, this result has been generalized by showing that if all P_i's are additive
more » ... ary, then generalized graph coloring is NP-hard, with the only exception of recognising bipartite graphs. Clearly, a similar result follows when all the P_i's are co-additive. In this paper, we study the problem where we have a mixture of additive and co-additive classes, presenting several new results dealing both with NP-hard and polynomial-time solvable instances of the problem.
arXiv:math/0306178v1 fatcat:xuzu6r3dxjbalmpofrnm524kvu