Decomposing and Clique‐Coloring (Diamond, Odd‐Hole)‐Free Graphs
Maria Chudnovsky, Irene Lo · Journal of Graph Theory · 2016
Abstract A diamond is a graph on vertices with exactly one pair of nonadjacent vertices, and an odd hole is an induced cycle of odd length greater than 3. If G and H are graphs, G is H‐free if no induced subgraph of G is isomorphic to H. A clique‐coloring of G is an assignment of colors to the vertices of G such that no inclusion‐wise maximal clique of size at least 2 is monochromatic. We show that every (diamond, odd‐hole)‐free graph is 3‐clique‐colorable, answering a question of Bacsó et al. (SIAM J Discrete Math 17(3) (2004), 361–376).