Odd wheels in graphs

  • Authors:

  • Baoguang Xu;Guoping Jin;Zhenhong Liu

  • Affiliations:

  • Institute of Policy and Management, Chinese Academy Sciences, Beijing, People's Republic of China;Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, University of Cambridge, Cambridge, United Kingdom;Institute of Systems Science, Chinese Academy Sciences, Beijing, People's Republic of China

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2002

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Abstract

For k ≥ 1 the odd wheel of 2k + 1 spokes, denoted by W2k+1, is the graph obtained from a cycle of length 2k + 1 by adding a new vertex and joining it to all vertices of the cycle. In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes.