A generalization of Dirac's theorem: Subdivisions of wheels

In this paper, we prove that if every vertex of a simple graph has degree at least δ , then it has a subgraph that is isomorphic to a subdivision of a δ -wheel. We then extend a result of Dirac showing that every graph with a chromatic number exceeding n has a subgraph that is a subdivision of the n...

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Bibliographic Details
Published inDiscrete mathematics Vol. 297; no. 1; pp. 202 - 205
Main Author Turner, Galen E.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 28.07.2005
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Minimum vertex degree
Minor
Sciences and techniques of general use
Subdivision
Topological-minor
Wheel
Wheel
Minimum vertex degree
Minor
Subdivision
Topological-minor
Topological minor
Vertex(graph)
Chromatic graph
Chromatic number
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Summary:In this paper, we prove that if every vertex of a simple graph has degree at least δ , then it has a subgraph that is isomorphic to a subdivision of a δ -wheel. We then extend a result of Dirac showing that every graph with a chromatic number exceeding n has a subgraph that is a subdivision of the n-wheel.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2005.05.003