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arXiv · 2206.03571

An excluded minor theorem for the Wagner graph plus an edge

Yuqi Xu·Weihua Yang
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Abstract

Let $V_{8}+e$ denote the unique graph obtained from the Wagner graph, also known as $V_{8}$, by adding an edge between two vertices of distance 3 on the Hamilton cycle, which is exactly a split of a minor of the Petersen graph. A complete characterization of all internally 4-connected graphs with no $V_{8}$ minor is given in [J. Maharry and N. Robertson, The structure of graphs not topologically containing the Wagner graph, J. Combin. Theory Ser. B 121 (2016) 398-420]. In this paper we characterize all internally 4-connected graphs with no $V_{8}+e$ minor.

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Yuqi Xu, Weihua Yang. 2022-05-24. An excluded minor theorem for the Wagner graph plus an edge. https://arxiv.org/abs/2206.03571

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