We show that the maximum induced matching problem can be solved on hhd-free graphs in O(m2) time; hhd-free graphs generalize chordal graphs and the previous best bound was O(m3). hen, we consider a technique used by Brandstädt and Hoàng (2008) [4] to solve the problem on chordal graphs. Extending this, we show that for a subclass of hhd-free graphs that is more general than chordal graphs the problem can be solved in linear time. We also present examples to demonstrate the tightness of our results.

Highlights

• Faster algorithm to find a largest induced matching in an hhd-free graph is given.
• For a superclass of chordal graphs, a linear time algorithm for the problem is given.
• Examples are presented to demonstrate the tightness of results.