Subdivisions in apex graphs

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Erscheinungsjahr:
2012
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Text
Schlagworte:
  • Article
  • Article
Beschreibung:
  • The Kelmans-Seymour conjecture states that every 5-connected nonplanar graph contains 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 every 5-connected nonplanar graph containing K-4(-) or K-2,K-3 as a subgraph has a subdivided K-5. Recently, Ma and Yu showed that every 5-connected nonplanar graph containing K-4(-) as a subgraph has a subdivided K-5. We take interest in K-2,K-3 and prove that every 5-connected nonplanar apex graph containing K-2,K-3 as a subgraph contains a subdivided K-5. The result of Ma and Yu can be used in a short discharging argument to prove that every 5-connected nonplanar apex graph contains a subdivided K-5; here we propose a longer proof whose merit is that it avoids the use of discharging and employs a more structural approach; consequently it is more amenable to generalization.
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  • info:eu-repo/semantics/restrictedAccess
Quellsystem:
Forschungsinformationssystem der UHH

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oai:www.edit.fis.uni-hamburg.de:publications/afbe1565-7aeb-4beb-8cba-a339d33c6e88