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.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Catherine S. Greenhill, Andrzej Rucinski
• Keywords: Colours, COMBINATORICS 2006, Edges Incident, Proper Edge