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Keywords:

  • circular chromatic index;
  • regular graphs;
  • line graphs

Abstract

The circular chromatic index of a graph G, written inline image, is the minimum r permitting a function inline image such that inline image whenever e and inline image are adjacent. It is known that for any inline image, there is a 3-regular simple graph G with inline image. This article proves the following results: Assume inline image is an odd integer. For any inline image, there is an n-regular simple graph G with inline image. For any inline image, there is an n-regular multigraph G with inline image.