### 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/5 edges); G has arbitrary large girth.

Original language | English |
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Pages (from-to) | 139-146 |

Number of pages | 8 |

Journal | Graphs and Combinatorics |

Volume | 13 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1997 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Chen, G., Erdos, P., Gyárfás, A., & Schelp, R. H. (1997). A class of edge critical 4-chromatic graphs.

*Graphs and Combinatorics*,*13*(2), 139-146. https://doi.org/10.1007/BF03352991