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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:1, 125-129

Volume 24, No 1, 2017, P. 21-30

UDC 519.8
E. I. Vasilyeva and A. V. Pyatkin
On list incidentor $(k, l)$-colorings

Abstract:
A proper incidentor coloring is called a $(k, l)$-coloring if the difference between the colors of the final and initial incidentors ranges between $k$ and $l$. In the list variant, the extra restriction is added: The color of each incidentor must belong to the set of admissible colors of the arc. In order to make this restriction reasonable we assume that the set of admissible colors for each arc is an integer interval. The minimum length of the interval that guarantees the existence of a list incidentor $(k, l)$-coloring is called a list incidentor $(k, l)$-chromatic number. Some bounds for the list incidentor $(k, l)$-chromatic number are proved for multigraphs of degree 2 and 4.
Bibliogr. 13.

Keywords: list coloring, incidentor, $(k, l)$-coloring.

DOI: 10.17377/daio.2017.24.542

Ekaterina I. Vasilyeva 2
Artem V. Pyatkin 1,2

1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: ekaterinavasilyeva93@gmail.com, artem@math.nsc.ru

Received 24 May 2016
Revised 6 June 2016

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