A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs
Babak Ghanbari, Robert \v{S}\'amal
TL;DR
This paper introduces a near-linear-time algorithm for finding a perfect matching in bridgeless cubic graphs that intersects every 3-edge-cut exactly once, improving efficiency over previous algorithms.
Contribution
The paper presents a novel near-linear-time algorithm for perfect matchings in bridgeless cubic graphs, utilizing cactus representations and efficient update procedures.
Findings
The algorithm operates in near-linear time.
It finds perfect matchings intersecting all 3-edge-cuts exactly once.
It improves upon previous cubic and earlier algorithms.
Abstract
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.
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