## Abstract Define the partial join of two graphs to be some graph arising from their disjoint union by adding a set of new edges each joining a vertex of the first graph and a vertex of the second one. We characterize all colourβcritical graphs being partial joins of a complete graph and an odd cy
On a class of completable partial edge-colourings
β Scribed by Alexander Rosa
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 555 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0166-218X
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Grossman and Ha ggkvist gave a sufficient condition under which a two-edgecoloured graph must have an alternating cycle (i.e., a cycle in which no two consecutive edges have the same colour). We extend their result to edge-coloured graphs with any number of colours. That is, we show that if there is