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COMBINATORICS
2006

Neighbour-Distinguishing Edge Colourings of Random Regular Graphs

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Neighbour-Distinguishing Edge Colourings of Random Regular Graphs
A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to the set of colours appearing on the edges incident with w. Let ndi(G) be the least number of colours required for a proper neighbour-distinguishing edge colouring of G. We prove that for d 4, a random d-regular graph G on n vertices asymptotically almost surely satisfies ndi(G) 3d/2 . This verifies a conjecture of Zhang, Liu and Wang for almost all 4-regular graphs.
Catherine S. Greenhill, Andrzej Rucinski
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Catherine S. Greenhill, Andrzej Rucinski
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