Perfect coloring and linearly χ-bound P 6 -free graphs

We derive decomposition theorems for P6, K1 + P4-free graphs, P5, K1 + P4-free graphs and P5, K1 + C4-free graphs, and deduce linear χ-binding functions for these classes of graphs (here, Pn (Cn) denotes the path (cycle) on n vertices and K1 + G denotes the graph obtained from G by adding a new vertex and joining it with every vertex of G). Using the same techniques, we also obtain an optimal χ-binding function for P5, C4-free graphs which is an improvement over that given in [J. L. Fouquet, V. Giakoumakis, F. Maire, and H. Thuillier, [1995], Discrete Math, 146, 33–44.]. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 293–306, 2007