A generalization of Dirac's theorem: Subdivisions of wheels

• Published in: Discrete mathematics Vol. 297; no. 1; pp. 202 - 205
• Main Author: Turner, Galen E.
• Format: Journal Article
• Language: English
• 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

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...