An improved algorithm for the longest induced path problem on image-chordal graphs

Gavril [F. Gavril, Algorithms for maximum weight induced paths, Information Processing Letters 81 (2002) 203–208] showed that the length of a longest induced path for graphs having no induced cycles on more than image vertices can be computed in image time where image and image denote the number of vertices and edges, respectively. In this paper, we present an image time algorithm for the same problem.