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A Class of Edge Critical 4-Chromatic Graphs

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Abstract

We consider several constructions of edge critical 4-chromatic graphs which can be written as the union of a bipartite graph and a matching. In particular we construct such a graph G with each of the following properties: G can be contracted to a given critical 4-chromatic graph; for each n ≥ 7, G has n vertices and three matching edges (it is also shown that such graphs must have at least \({{8n} \over 5}\) edges); G has arbitrary large girth.

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Authors and Affiliations

  1. Georgia State University, Atlanta, GA, 30303-3083, USA

    Guantao Chen

  2. Mathematical Institute, Hungarian Academy of Sciences, Hungary

    Paul Erdős

  3. Computer and Automation Research Institute, Hungarian Academy of Sciences, University of Memphis, USA

    András Gyárfás

  4. Department of Mathematics, University of Memphis, Memphis, TN, 38152, USA

    R. H. Schelp

Authors
  1. Guantao Chen
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  2. Paul Erdős
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  3. András Gyárfás
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  4. R. H. Schelp
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Chen, G., Erdős, P., Gyárfás, A. et al. A Class of Edge Critical 4-Chromatic Graphs. Graphs and Combinatorics 13, 139–146 (1997). https://doi.org/10.1007/BF03352991

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  • DOI: https://doi.org/10.1007/BF03352991

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