Polynomial enumeration of chordless cycles on cyclically orientable graphs

Abstract

In a finite 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 have the advantage of finding each chordless cycle only once in time complexity $\mathcal{O}(n^2)$ in the input size, where $n$ is the number of vertices.