Planar wheel-like bricks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910672684580864 |
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| author | Lu, Fuliang Xue, Jinxin |
| author_facet | Lu, Fuliang Xue, Jinxin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Planar wheel-like bricks Lu, Fuliang Xue, Jinxin Combinatorics 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. |
| title | Planar wheel-like bricks |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.20692 |