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arXiv · 2410.20692

Planar wheel-like bricks

Fuliang Lu·Jinxin Xue
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Abstract

An edge e in a matching covered graph G is removable if G-e is matching covered; a pair {e; f} of edges of G is a removable doubleton if G-e-f is matching covered, but neither G-e nor G-f is. Removable edges and removable doubletons are called removable classes, which was introduced by Lovasz and Plummer in connection with ear decompositions of matching covered graphs. A brick is a nonbipartite matching covered graph without nontrivial tight cuts. A brick G is wheel-like if G has a vertex h, such that every removable class of G has an edge incident with h. Lucchesi and Murty conjectured that every planar wheel-like brick is an odd wheel. We present a proof of this conjecture in this paper.

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Fuliang Lu, Jinxin Xue. 2024-10-28. Planar wheel-like bricks. https://arxiv.org/abs/2410.20692

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