### 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 |

Publication status | Published - 1997 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics

### Cite this

*Graphs and Combinatorics*,

*13*(2), 139-146.

**A class of edge critical 4-chromatic graphs.** / Chen, Guantao; Erdős, P.; Gyárfás, A.; Schelp, R. H.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 13, no. 2, pp. 139-146.

}

TY - JOUR

T1 - A class of edge critical 4-chromatic graphs

AU - Chen, Guantao

AU - Erdős, P.

AU - Gyárfás, A.

AU - Schelp, R. H.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=27644538997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644538997&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27644538997

VL - 13

SP - 139

EP - 146

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 2

ER -