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Decomposing and Clique‐Coloring (Diamond, Odd‐Hole)‐Free Graphs
Author(s) -
Chudnovsky Maria,
Lo Irene
Publication year - 2017
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22110
Subject(s) - combinatorics , mathematics , induced subgraph , monochromatic color , graph , clique , clique number , discrete mathematics , vertex (graph theory) , physics , optics
A diamond is a graph on four 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).