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A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs

Authors: Babak Ghanbari and Robert Šámal

Published in: LIPIcs, Volume 386, 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)


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 as

Babak Ghanbari and Robert Šámal. A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{ghanbari_et_al:LIPIcs.MFCS.2026.11,
  author =	{Ghanbari, Babak and \v{S}\'{a}mal, Robert},
  title =	{{A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs}},
  booktitle =	{51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-442-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{386},
  editor =	{Kouck\'{y}, Michal and Petrișan, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2026.11},
  URN =		{urn:nbn:de:0030-drops-273922},
  doi =		{10.4230/LIPIcs.MFCS.2026.11},
  annote =	{Keywords: bridgeless cubic graphs, well-spread perfect matching, edge cuts, cactus representation}
}
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