Odd edge-colorability of subcubic graphs
Risto Atanasov, Mirko Petruševski, Riste Škrekovski · Ars Mathematica Contemporanea · 2016
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.