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A Combined Logarithmic Bound on the Chromatic Index of Multigraphs

Authors


  • Contract grant sponsor: Illinois State University.

Abstract

For a multigraph G, the integer round-up math formula of the fractional chromatic index math formula provides a good general lower bound for the chromatic index math formula. For an upper bound, Kahn 1996 showed that for any real math formula there exists a positive integer N so that math formula whenever math formula. We show that for any multigraph G with order n and at least one edge, math formula). This gives the following natural generalization of Kahn's result: for any positive reals math formula, there exists a positive integer N so that math formula + c math formula whenever math formula. We also compare the upper bound found here to other leading upper bounds.

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