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arxiv: 1012.5792 · v1 · pith:LNWZ2JOEnew · submitted 2010-12-28 · 🧮 math.CO

Subdivisions in apex graphs

classification 🧮 math.CO
keywords connectednonplanarsubdividedcontaininggraphsubgraphapexconjecture
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The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided $K_{_5}$. Certain questions of Mader propose a "plan" towards a possible resolution of this conjecture. One part of this plan is to show that a 5-connected nonplanar graph containing $K^-_{_4}$ or $K_{_{2,3}}$ as a subgraph has a subdivided $K_{_5}$. Recently, Ma and Yu showed that a 5-connected nonplanar graph containing $K^-_{_4}$ as a subgraph has a subdivided $K_{_5}$. We take interest in $K_{_{2,3}}$ and prove that a 5-connected nonplanar apex graph containing $K_{_{2,3}}$ as a subgraph has a subdivided $K_{_5}$

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