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The generalized acyclic edge chromatic number of random regular graphs
Author(s) -
Gerke Stefanie,
Greenhill Catherine,
Wormald Nicholas
Publication year - 2006
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20167
Subject(s) - combinatorics , mathematics , chromatic scale , edge coloring , brooks' theorem , discrete mathematics , random graph , graph , foster graph , critical graph , upper and lower bounds , graph power , line graph , mathematical analysis
The r ‐acyclic edge chromatic number of a graph is defined to be the minimum number of colors required to produce an edge coloring of the graph such that adjacent edges receive different colors and every cycle C has at least min(| C |, r ) colors. We show that ( r − 2) d is asymptotically almost surely (a.a.s.) an upper bound on the r ‐acyclic edge chromatic number of a random d ‐regular graph, for all constants r ≥ 4 and d ≥ 2. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 101–125, 2006
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