A precolouring extension of Vizing's theorem

António Girão, Ross J. Kang
2019 Journal of Graph Theory  
Fix a palette of Δ + 1 colors, a graph with maximum degree Δ, and a subset M of the edge set with minimum distance between edges at least 9. If the edges of M are arbitrarily precoloured from , then there is guaranteed to be a proper edge-coloring using only colors from that extends the precolouring on M to the entire graph. This result is a first general precolouring extension form of Vizing's theorem, and it proves a conjecture of Albertson and Moore under a slightly stronger distance
more » ... ent. We also show that the condition on the distance can be lowered to 5 when the graph contains no cycle of length 5.
doi:10.1002/jgt.22451 fatcat:pnlfhivdeva4tedhn622og467e