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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics