Circular chromatic index of small graphs
Abstract
We systematically determine circular chromatic index of small graphs and multigraphs with maximum degree 4, 5, 6 (and also their number for a given small order). We construct several infinite families of such graphs with circular chromatic index in the set \ + 1/2, + 2/3, + 3/4, + 1\. Our results refute edge-connectivity variants of the ``Upper Gap Conjecture'' (about the non-existence of graphs with circular chromatic index just below + 1).
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