Odd edge-colorability of subcubic graphs - Atanasov, Risto (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 ?$χ_o^{′}(G)$?. These notions were introduced by L. Pyber L. Pyber, Covering the edges of a graph by . . ., in: Sets, graphs and numbers (Budapest, 1991), North-Holland, Amsterdam, volume 60 of Colloq. Math. Soc. János Bolyai, pp. 583-610, 1992, 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: lihi kromatični indeks; liho barvanje povezav; liho pokritje povezav; odd chromatic index; odd edge-coloring; odd edge-covering; subcubic graph; subkubičen graf; T-join; T-spoj