Efficient algorithms for Petersen's matching theorem

Petersen's theorem is a classic result in matching theory from 1891, stating that every 3-regular bridgeless graph has a perfect matching. Our work explores efficient algorithms for finding perfect matchings in such graphs. Previously the only relevant matching algorithms were for general graphs, and the fastest algorithm ran in O(n(3/2)) time. We have developed an O(n log(4) n)-time algorithm for matching in a 3-regular bridgeless graph. when the graph is also planar, we have as the main result of our paper an optimal O( n)-time algorithm. We present three applications of this result, terrain guarding, adaptive mesh refinement, and quadrangulation.