
TL;DR
This paper proves that 5-connected nonplanar apex graphs containing a $K_{2,3}$ subgraph necessarily have a subdivided $K_5$, advancing understanding of the Kelmans-Seymour conjecture.
Contribution
It establishes that such apex graphs with a $K_{2,3}$ subgraph contain a subdivided $K_5$, filling a gap in the plan towards the conjecture.
Findings
Proves the existence of subdivided $K_5$ in the specified graphs.
Extends previous results from $K^-_4$ to $K_{2,3}$.
Supports the plan to resolve the Kelmans-Seymour conjecture.
Abstract
The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided . 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 or as a subgraph has a subdivided . Recently, Ma and Yu showed that a 5-connected nonplanar graph containing as a subgraph has a subdivided . We take interest in and prove that a 5-connected nonplanar apex graph containing as a subgraph has a subdivided
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Interconnection Networks and Systems
