A Note on Enumeration of 3-Edge-Connected Spanning Subgraphs in Plane Graphs

Abstract

This paper deals with the problem of enumerating 3-edge-connected spanning subgraphs of an input plane graph. In 2018, Yamanaka et al. proposed two enumeration algorithms for such a problem. Their algorithm generates each 2-edge-connected spanning subgraph of a given plane graph with n vertices in O(n) time, and another one generates each k-edge-connected spanning subgraph of a general graph with m edges in O(mT) time, where T is the running time to check the k-edge connectivity of a graph. This paper focuses on the case of the 3-edge-connectivity in a plane graph. We give an algorithm which generates each 3-edge-connected spanning subgraph of the input plane graph in O(n2) time. This time complexity is the same as the algorithm by Yamanaka et al., but our algorithm is simpler than theirs.