Artem Pyatkin
On incidentor colorings of multigraphs (review)

An incidentor in a directed or undirected multigraph is an ordered pair
of a vertex and an arc incident with it. It is convenient to treat
incidentor as a half of an arc incident with a vertex. Two incidentors
of the same arc are called mated. Two incidentors are adjacent if they
adjoin the same vertex. The incidentor coloring problem (indeed, a class
of problems) is to color all incidentors of a given multigraph with the
minimum number of colors satisfying some restrictions on colors of
adjacent and mated incidentors.

The review of various results on the incidentor coloring is given in the
talk.