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JOURNALS // Diskretnyi Analiz i Issledovanie Operatsii // Archive

Diskretn. Anal. Issled. Oper., 2017 Volume 24, Issue 4, Pages 34–46 (Mi da880)

On $(1,l)$-coloring of incidentors of multigraphs

M. O. Golovacheva, A. V. Pyatkinba

a Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: It is proved that if $l$ is at least $\Delta/2-1$ then $(1,l)$-chromatic number of an arbitrary multigraph of maximum degree $\Delta$ is at most $\Delta+1$. Moreover, it is proved that the incidentors of every directed prism can be colored in four colors so that every two adjacent incidentors are colored distinctly and the difference between the colors of the final and initial incidentors of each arc is $1$. Illustr. 1, bibliogr. 10.

Keywords: incidentor coloring, $(1,l)$-coloring, prism.

UDC: 519.174

Received: 22.03.2017
Revised: 10.04.2017

DOI: 10.17377/daio.2017.24.572


 English version:
Journal of Applied and Industrial Mathematics, 2017, 11:4, 514–520

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© Steklov Math. Inst. of RAS, 2025