Graphs and Combinatorics

, Volume 13, Issue 2, pp 139–146 | Cite as

A Class of Edge Critical 4-Chromatic Graphs

  • Guantao Chen
  • Paul Erdős
  • András Gyárfás
  • R. H. Schelp


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.


Bipartite Graph Chromatic Number Critical Graph Partite Class Matching Edge 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Guantao Chen
    • 1
  • Paul Erdős
    • 2
  • András Gyárfás
    • 3
  • R. H. Schelp
    • 4
  1. 1.Georgia State UniversityAtlantaUSA
  2. 2.Mathematical InstituteHungarian Academy of SciencesHungary
  3. 3.Computer and Automation Research Institute, Hungarian Academy of SciencesUniversity of MemphisUSA
  4. 4.Department of MathematicsUniversity of MemphisMemphisUSA

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