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Optimal acyclic edge-coloring of cubic graphs

✍ Scribed by Lars Døvling Andersen; Edita Máčajová;; Ján Mazák

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 194 KB
Volume: 71
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20650

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✦ Synopsis

An acyclic edge‐coloring of a graph is a proper edge‐coloring such that the subgraph induced by the edges of any two colors is acyclic. The acyclic chromatic index of a graph G is the smallest number of colors in an acyclic edge‐coloring of G. We prove that the acyclic chromatic index of a connected cubic graph G is 4, unless G is K~4~ or K~3,3~; the acyclic chromatic index of K~4~ and K~3,3~ is 5. This result has previously been published by Fiamčík, but his published proof was erroneous.

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