Abstract
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⩽2 t( ω−1) for ω⩾2. Overlap graphs satisfy χ⩽2 ω ω 2( ω−1).
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