A Combined Logarithmic Bound on the Chromatic Index of a Multigraph

Details A Combined Logarithmic Bound on the Chromatic Index of a Multigraph A Combined Logarithmic Bound on the Chromatic Index of a Multigraph

2010-12-22

arxiv.org/abs/1012.5003v2

Mathematics

Combinatorics

Scientific paper

For a multigraph G, the integer round-up phi(G) of the fractional chromatic index yields a good general lower bound for the chromatic index . For an upper bound, Kahn showed that for any real c > 0 there exists a positive integer N so that the chromatic index is less than (1+c)*phi(G) whenever the fractional index > N. We show the amount by which the chromatic index can surpass phi(G) is in fact logarithmic, by showing that for any multigraph G with order n > 3 and at least one edge, the chromatic index is less than phi(G) + log (min {(n+1)/3, phi(G)}) .

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