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

Authors Babak Ghanbari , Robert Šámal

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LIPIcs.MFCS.2026.11.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Discrete mathematics
Keywords
  • bridgeless cubic graphs
  • well-spread perfect matching
  • edge cuts
  • cactus representation

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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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.MFCS.2026.11

Author Details

Babak Ghanbari
  • Computer Science Institute of Charles University, Prague, Czech Republic
Robert Šámal
  • Computer Science Institute of Charles University, Prague, Czech Republic

Funding

Supported by grant 25-16627S of the Czech Science Foundation.

Acknowledgements

We thank Matt DeVos for helpful discussion.

References

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