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There exist oriented planar graphs with oriented chromatic number at least sixteen
Information Processing Letters, 2002 Abstract We prove that there exist oriented planar graphs with oriented chromatic number at least 16. Using a result of Raspaud and Sopena [Inform. Process. Lett. 51 (1994) 171–174], this gives that the oriented chromatic number of the family of oriented planar graphs lies between 16 and 80.
Éric Sopena
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On the maximum average degree and the oriented chromatic number of a graph [PDF]
Discrete Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jaroslav Nešetřil +2 more
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The oriented chromatic number of Halin graphs [PDF]
Information Processing Letters, 2014 Oriented chromatic number of an oriented graph $G$ is the minimum order of an oriented graph $H$ such that $G$ admits a homomorphism to $H$. The oriented chromatic number of an unoriented graph $G$ is the maximal chromatic number over all possible orientations of $G$.
Janusz Dybizbański +1 more
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The chromatic number of oriented graphs
Journal of Graph Theory, 1997In this paper the chromatic number of an oriented graph \(G\) (that is of an antisymmetric directed graph) is defined as the minimum order of an oriented graph \(H\) such that \(G\) admits a homomorphism to \(H\). It is shown that there exist oriented \(k\)-trees with chromatic number at least \(2^{k+1}-1\) and that every oriented \(k\)-tree has ...
Éric Sopena
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On the oriented chromatic number of Halin graphs
Information Processing Letters, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Éric Sopena
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A note on the oriented chromatic number of grids
Information Processing Letters, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrzej Szepietowski
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Acyclic and oriented chromatic numbers of graphs
Journal of Graph Theory, 1997The authors study relations between the oriented chromatic number of a graph and the chromatic number, the arboricity, the (bounded) acyclic chromatic number, the maximum vertex degree and the genus. It is shown (among other results) that if \(G\) is a graph with maximum degree \(h\), then the oriented chromatic number of \(G\) is at most \(2h^22^h ...
Éric Sopena, A V Kostochka
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Subdivisions of oriented cycles in Hamiltonian digraphs with small chromatic number
Discrete Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mouhamad El Joubbeh
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On the oriented chromatic index of oriented graphs
Journal of Graph Theory, 2008 International audienceA homomorphism from an oriented graph G to an oriented graph H is a mapping f from the set of vertices of G to the set of vertices of H such that f(U)f(V) is an arc in H whenever uv is an arc in G. The oriented chromatic index of an
Pascal Ochem +2 more
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Efficient computation of the oriented chromatic number of recursively defined digraphs [PDF]
Theoretical Computer Science, 2021 25 pages.
Frank Gurski, Dominique Komander
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