Abstract
A maximal edge-coloring of a graph G of order n is a proper edge-coloring of G with \(\chi '(K_n)\) colors such that no edge of the complement \(\overline{G}\) of G can be attached to G without violating conditions of a proper edge-coloring. We almost completely determine sets of all sizes of graphs which admit maximal edge-colorings.
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Meszka, M., Tyniec, M. Maximal Edge-Colorings of Graphs. Graphs and Combinatorics 33, 1451–1458 (2017). https://doi.org/10.1007/s00373-017-1797-0
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DOI: https://doi.org/10.1007/s00373-017-1797-0