On coloring a class of claw-free and hole-twin-free graphs

Abstract

Hole-twins – graphs that arise when a vertex is added to a hole in such a way to form a twin with some vertex of the hole – were discussed in a recent paper by Dai, Foley, and Hoàng where it was shown that there is a polynomial time algorithm to color ( c l a w , 4 K 1 , hole-twin)-free graphs. We continue our investigation of hole-twin-free graphs and show the coloring problem for ( c l a w , P 7 , hole-twin)-free graphs is also polynomial-time solvable.