Abstract
In this paper, we introduce a new family of graphs which is a subclass of chordal graphs as well as a superclass of interval graphs and study it. Myung [8] proposed an algorithm for the minimum clique partitioning problem with constrained bounds in weighted interval graphs. We extend the family of interval graphs to the family of so called “interval-like graphs” to which Myung's algorithm is applicable and show that bull-free chordal graphs and diamond-free chordal graphs are interval-like graphs.
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