COMPUTING THE GIRTH OF A PLANAR GRAPH IN LINEAR TIME
The girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first nontrivial algorithm for the problem, given by Djidjev, runs in O(n(5/4) log n) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(n log(2) n). Weimann and Yuster further reduced the running time to O(n log n). In this paper, we solve the problem in O(n) time.
planar graphs paths and cycles graph algorithms data structures