Speaker: Borut Lužar
Title: From proper to strong edge-colorings of subcubic graphs
Abstract:
    In the talk, we will discuss edge-colorings of (sub)cubic graphs.
	Namely, we will consider edge-colorings in which we work with two types of colors:
	the proper and the strong colors. 
	The edges colored with the same proper color form a matching (no two edges are incident),
	and the edges colored with the same strong color form an induced matching (no two edges are incident to a common edge).
	Clearly, when all the colors are proper, 
	the edge-coloring of a graph is proper, and if all the colors are required to be strong, 
	we have a strong edge-coloring.
	The tight upper bounds for the chromatic indices of the above two extremal colorings are long established,
	thus we will focus to edge-colorings with combinations of proper and strong colors.
	Such colorings have been investigated before, but only as a tool to obtain results for other types of colorings.
	Systematically, they have been introduced just recently by Gastineau and Togni as an edge-coloring variation of $S$-packing colorings~\cite{GasTog19}.
	We will present results on the topic and give a number of open problems. 
    Joint work with Herve Hocquard and Dimitri Lajou.

\bibitem{GasTog19} N. Gastineau, O. Togni, On $S$-packing edge-colorings of cubic graphs, Discrete Appl. Math. 259 (2019), 63--75.
\bibitem{HerLajLuz21} H. Hocquard, D. Lajou, B. Lu\v{z}ar, Between proper and strong edge-colorings of subcubic graphs, \href{https://arxiv.org/abs/2011.02175}{arXiv preprint 2011.02175}, 2020.