A k-critical (multi-) graph G has maximum degree k, chromatic index Ο (G) = k + 1, and Ο (G -e) < k + 1 for each edge e of G. For each k β₯ 3, we construct k-critical (multi-) graphs with certain properties to obtain counterexamples to some well-known conjectures.
Vertex-splitting and chromatic index critical graphs
β Scribed by A.J.W. Hilton; C. Zhao
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 477 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0166-218X
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β¦ Synopsis
We study graphs which are critical with respect to the chromatic index. We relate these to the Overfull Conjecture and we study in particular their construction from regular graphs by subdividing an edge or by splitting a vertex.
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