Description
Circular colourings are a relaxation of proper graph colourings where we allow real numbers as colours. They serve as a model for scheduling problems in which we have arbitrary starting times instead of aligned slots. We provide an overview of computational methods we successfully used to determine circular chromatic index of small graphs and discuss recent results related to the Upper Gap Conjecture which asserts that certain ``high'' values of circular chromatic index are not attainable by any graph. In particular, we determine the circular chromatic index of small graphs with maximum degree 4, 5, 6 and refute certain variants of the conjecture.
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