A Linear Algorithm for the Group Path Problem on Chordal Graphs

Abstract Assume that each edge of a graph G=(V,E) is given a weight, which is an element of some group G . The weight of a path P is defined as the product of the weights of the edges along P. The group path problem is to find a chordless path of a given weight between two given vertices. It generalizes the parity path problem considered by Hsu. We show that the recognition problem associated with the group path problem is NP-complete in general, and present an O(| G |·|E|+|V|) time algorithm for the group path problem on a chordal graph.