A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs
Data Structures and Algorithms
2026-05-04 v1 Discrete Mathematics
Combinatorics
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.
Cite
@article{arxiv.2605.00710,
title = {A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs},
author = {Babak Ghanbari and Robert Šámal},
journal= {arXiv preprint arXiv:2605.00710},
year = {2026}
}