On an Edge Precoloring Conjecture

Abstract

Edwards, van den Heuvel, Kang, and Sereni conjectured the following strengthening of Vizing's Theorem: let G be a simple graph, and let K = (G) + 1. For any matching M in G and any precoloring of the edges in M using the colors \1, …, K\, there is some proper K-edge-coloring of G extending the given precoloring. We give an infinite family of counterexamples to this conjecture, and prove a weaker version of the conjecture proposed in the same work.

0

Turn this paper into a lesson

ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…