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Two results on the digraph chromatic numberHarutyunyan, Ararat, 1984- ; Mohar, Bojan, 1956-It is known (Bollobás (1978); Kostochka and Mazurova (1977)) that there exist graphs of maximum degree ▫$\Delta$▫ and of arbitrarily large girth whose chromatic number is at least ▫$c \Delta / \log ... \Delta$▫. We show an analogous result for digraphs where the chromatic number of a digraph ▫$D$▫ is defined as the minimum integer ▫$k$▫ so that ▫$V(D)$▫ can be partitioned into ▫$k$▫ acyclic sets, and the girth is the length of the shortest cycle in the corresponding undirected graph. It is also shown, in the same vein as an old result of Erdős(1962), that there are digraphs with arbitrarily large chromatic number where every large subset of vertices is 2-colorable.Source: Discrete mathematics. - ISSN 0012-365X (Vol. 312, iss. 10, 2012, str. 1823-1826)Type of material - article, component partPublish date - 2012Language - englishCOBISS.SI-ID - 16283481
Author
Harutyunyan, Ararat, 1984- |
Mohar, Bojan, 1956-
Topics
matematika |
teorija grafov |
kromatično število |
usmerjen graf |
barvanje |
ožina |
mathematics |
graph theory |
chromatic number |
digraph |
digraph coloring |
dichromatic number |
girth
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Harutyunyan, Ararat, 1984- | |
Mohar, Bojan, 1956- | 01931 |
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