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  "coverImage": {
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  "path": "/abs/2605.00710v1",
  "publishedAt": "2026-05-04T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Babak Ghanbari",
    "Robert Šámal"
  ],
  "textContent": "**Authors:** Babak Ghanbari, Robert Šámal\n\nWe 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.",
  "title": "A Near-Linear-Time Algorithm for Finding a Well-Spread Perfect Matching in Bridgeless Cubic Graphs"
}