Let χ(G) and ω(G) denote the chromatic number and clique number of a graph G. We prove that χ can be bounded by a function of ω for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line) satisfy χ≤2t(ω-1) for ω≥2. Overlap graphs satisfy χ≤2ωω2(ω-1).
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics