On the maximum independent set problem in graphs of bounded maximum degree

Abstract

We consider the maximum independent set (MIS) problem, i.e.. the problem asking for a vertex subset of maximum cardinality of a graph such that no two vertices in this set are adjacent. The problem is known to be NP-hard in general, even if restricted on graphs of maximum degree at most A for a given integer Δ > 3. i.e.. every vertex is of degree at most Δ. We try to figure out some bounded maximum degree graph classes, under which the problem can be solved in polynomial time.