Results 11 to 20 of about 9,631,849 (193)
The oriented chromatic number of the hexagonal grid is 6 [PDF]
Discrete Applied Mathematics, 2023 8 pages, 5 ...
Lozano, Antoni
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On the Oriented Game Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2000 We consider the oriented version of a coloring game introduced by Bodlaender [On the complexity of some coloring games, Internat. J. Found. Comput. Sci. 2 (1991), 133–147]. We prove that every oriented path has oriented game chromatic number at most 7 (and this bound is tight), that every oriented tree has oriented game chromatic number at most 19 and ...
Jaroslav Nesetril, Éric Sopena
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On the oriented chromatic number of dense graphs [PDF]
Contributions to Discrete Mathematics, 2007 Let G be a graph with n vertices, m edges, average degree δ, and maximum degree Δ. The \emph{oriented chromatic number} of G is the maximum, taken over all orientations of G, of the minimum number of colours in a proper vertex colouring such that between every pair of colour classes all edges have the same orientation.
Wood, David R.
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The oriented chromatic number of some grids. [PDF]
Ann. UMCS Informatica, 2006 Artykuł z : Annales Universitatis Mariae Curie-Skłodowska, Sectio AI, Informatica, Vol. 5 (2006), s. 5-17 ; Artykuł z : Annales Universitatis Mariae Curie-Skłodowska, Sectio AI, Informatica, Vol. 5 (2006), s.
Bielak, Halina
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Upper oriented chromatic number of undirected graphs and oriented colorings of product graphs [PDF]
Discussiones Mathematicae Graph Theory, 2012 The oriented chromatic number of an oriented graph $\vec G$ is the minimum order of an oriented graph $\vev H$ such that $\vec G$ admits a homomorphism to $\vev H$. The oriented chromatic number of an undirected graph $G$ is then the greatest oriented chromatic number of its orientations. In this paper, we introduce the new notion of the upper oriented
Sopena, Eric
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Bounds for the (m,n)-mixed chromatic number and the oriented chromatic number
, 2013 We give new bounds for the (m,n)-mixed chromatic number and the oriented chromatic number of graphs.
Klostermeyer, William F. +3 more
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Forbidden Subgraph Colorings and the Oriented Chromatic Number
European Journal of Combinatorics, 2009 We present an improved upper bound of O(d^1^+^1^m^-^1) for the (2,F)-subgraph chromatic number @g"2","F(G) of any graph G of maximum degree d. Here, m denotes the minimum number of edges in any member of F. This bound is tight up to a (logd)^1^/^(^m^-^1^) multiplicative factor and improves the previous bound presented in Aravind and Subramanian (2011) [
N. R. Aravind, C. R. Subramanian 0001
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Oriented Chromatic Number of Cartesian Products and Strong Products of Paths [PDF]
Discussiones Mathematicae Graph Theory, 2019 An oriented coloring of an oriented graph G is a homomorphism from G to H such that H is without selfloops and arcs in opposite directions. We shall say that H is a coloring graph.
Dybizbański Janusz, Nenca Anna
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Subdivisions of oriented cycles in digraphs with large chromatic number [PDF]
Journal of Graph Theory, 2018 AbstractAn oriented cycle is an orientation of a undirected cycle. We first show that for any oriented cycle C, there are digraphs containing no subdivision of C (as a subdigraph) and arbitrarily large chromatic number. In contrast, we show that for any C a cycle with two blocks, every strongly connected digraph with sufficiently large chromatic number
Cohen, Nathann +3 more
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Subdivisions of oriented cycles in digraphs with large chromatic number [PDF]
, 2016 International audienceExtended Abstract The chromatic number χ(D) of a digraph D is the chromatic number of its underlying graph. An oriented cycle is an orientation of a undirected cycle.
Lochet, William +3 more
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