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Winding number and circular 4-coloring of (signed) graphs


Concerning the recent notion of circular chromatic number of signed graphs, we introduce a bipartite analogue of the generalized Mycielski graphs, denoted BM k,2k−1 , having the following properties. It has k(2k − 1) + 1 vertices, its shortest negative cycle is of length 2k and its circular chromatic number is 4. In the course of proving our result, we also obtain a simpler proof of the fact that the generalized Mycielski graph M ℓ (C 2k+1) has circular chromatic number 4. The proof has the advantage that it illuminates, in an elementary manner, the strong relation between algebraic topology and graph coloring problems.
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hal-03840738 , version 1 (06-11-2022)


  • HAL Id : hal-03840738 , version 1


Reza Naserasr. Winding number and circular 4-coloring of (signed) graphs. 2022. ⟨hal-03840738⟩
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