A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs
This provides a faster algorithm for a key problem in graph theory, benefiting researchers working on perfect matchings and edge cuts in cubic graphs.
We present a near-linear-time algorithm for finding a perfect matching that intersects every 3-edge-cut in exactly one edge in bridgeless cubic graphs, improving over a previous cubic algorithm and extending to graphs with 2-edge-cuts.
We present a near-linear-time algorithm that, given a bridgeless cubic graph, finds a perfect matching intersecting every 3-edge-cut in exactly one edge. This improves over a cubic algorithm of Boyd et al. for the same problem, and over our previous algorithm, which worked only for 3-edge-connected graphs. The main ingredient is a cactus representation of the 2-edge-cuts, together with an efficient update procedure under 2-cut reductions.