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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.
Received: 22.03.2017 Revised: 10.04.2017
Citation:
M. O. Golovachev, A. V. Pyatkin, “On $(1,l)$-coloring of incidentors of multigraphs”, Diskretn. Anal. Issled. Oper., 24:4 (2017), 34–46; J. Appl. Industr. Math., 11:4 (2017), 514–520
Linking options:
https://www.mathnet.ru/eng/da880 https://www.mathnet.ru/eng/da/v24/i4/p34
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| Abstract page: | 306 | | Full-text PDF : | 90 | | References: | 63 | | First page: | 5 |
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