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arXiv · 2101.04730

Rooted prism-minors and disjoint cycles containing a specified edge

João Paulo Costalonga·Talmage James Reid·Haindong Wu
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Abstract

Dirac and Lov\'{a}sz independently characterized the $3$-connected graphs with no pair of vertex-disjoint cycles. Equivalently, they characterized all $3$-connected graphs with no prism-minors. In this paper, we completely characterize the $3$-connected graphs with an edge that is contained in the union of no pair of vertex-disjoint cycles. As applications, we answer the analogous questions for edge-disjoint cycles and for $4$-connected graphs and we completely characterize the $3$-connected graphs with no prism-minor using a specified edge.

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João Paulo Costalonga, Talmage James Reid, Haindong Wu. 2021-01-12. Rooted prism-minors and disjoint cycles containing a specified edge. https://arxiv.org/abs/2101.04730

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