Polynomial enumeration of chordless cycles on cyclically orientable graphs

Abstract

In a nite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an algorithm to enumerate all chordless cycles of such a graph. Compared to other similar algorithms, the proposed algorithm has the advantage of nding each chordless cycle only once in time complexity O(n2), where n is the number of vertices.