Odd edge-colorability of subcubic graphs

Risto Atanasov, Mirko Petruševski, Riste Škrekovski

Abstract


An edge-coloring of a graph G is said to be odd if for each vertex v of G and each color c, the vertex v either uses the color c an odd number of times or does not use it at all. The minimum number of colors needed for an odd edge-coloring of G is the odd chromatic index χʹo(G). These notions were introduced by Pyber, who showed that 4 colors suffice for an odd edge-coloring of any simple graph. In this paper, we consider loopless subcubic graphs, and give a complete characterization in terms of the value of their odd chromatic index.


Keywords


Subcubic graph, odd edge-coloring, odd chromatic index, odd edge-covering, T-join

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DOI: https://doi.org/10.26493/1855-3974.957.97c

ISSN: 1855-3974

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