On the Maximum Independent Set Problem in Subclasses of Planar Graphs

Abstract

The maximum independent set problem is known to be NP-hard in the class of planar graphs. In the present paper, we study its complexity in hereditary subclasses of planar graphs. In particular, by combining various techniques, we show that the problem is polynomially solvable in the class of S_1,2,k-free planar graphs, generalizing several previously known results. S_1,2,k is the graph consisting of three induced paths of lengths 1, 2 and k, with a common initial vertex.