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432,830
The Chromatic Number of Oriented Graphs
 J. Graph Theory
, 2001
"... . We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) dened as the minimum order of an oriented graph H such that G admits a homomorphism to H . We study the chromatic number of oriented ktrees and of oriented graphs with ..."
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Cited by 61 (20 self)
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. We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) dened as the minimum order of an oriented graph H such that G admits a homomorphism to H . We study the chromatic number of oriented ktrees and of oriented graphs
On oriented graph scores
"... Abstract. In this paper, we obtain some results concerning the scores in oriented graphs. Further, we give a new and direct proof of the Theorem on oriented graph scores due to Avery [1]. 1. ..."
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Cited by 2 (1 self)
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Abstract. In this paper, we obtain some results concerning the scores in oriented graphs. Further, we give a new and direct proof of the Theorem on oriented graph scores due to Avery [1]. 1.
Perfection in Oriented Graphs
, 2003
"... We consider the notion of perfection in the coloring of oriented graphs. Perfect graphs are very important in the field of algorithms, as many problems that are NPcomplete in general can be solved in polynomial time in perfect graphs. Our interest is to define an analog of perfection for oriented c ..."
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We consider the notion of perfection in the coloring of oriented graphs. Perfect graphs are very important in the field of algorithms, as many problems that are NPcomplete in general can be solved in polynomial time in perfect graphs. Our interest is to define an analog of perfection for oriented
Oriented Graph Coloring
 DISCRETE MATH
, 2001
"... An oriented kcoloring of an oriented graph G (that is a digraph with no cycle of length 2) is a partition of its vertex set into k subsets such that (i) no two adjacent vertices belong to the same subset and (ii) all the arcs between any two subsets have the same direction. We survey the main resu ..."
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Cited by 24 (5 self)
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An oriented kcoloring of an oriented graph G (that is a digraph with no cycle of length 2) is a partition of its vertex set into k subsets such that (i) no two adjacent vertices belong to the same subset and (ii) all the arcs between any two subsets have the same direction. We survey the main
On Stratified Domination in Oriented Graphs
"... An oriented graph is 2stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let H be a 2stratified oriented graph rooted at some blue vertex. An Hcoloring of an oriented graph D is a redblue co ..."
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An oriented graph is 2stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let H be a 2stratified oriented graph rooted at some blue vertex. An Hcoloring of an oriented graph D is a red
Cyclically Orientable Graphs
, 2005
"... Barot, Geiss and Zelevinsky define a notion of a “cyclically orientable graph ” and use it to devise a test for whether a cluster algebra is of finite type. Barot, Geiss and Zelivinsky’s work leaves open the question of giving an efficient characterization of cyclically orientable graphs. In this pa ..."
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Cited by 1 (0 self)
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Barot, Geiss and Zelevinsky define a notion of a “cyclically orientable graph ” and use it to devise a test for whether a cluster algebra is of finite type. Barot, Geiss and Zelivinsky’s work leaves open the question of giving an efficient characterization of cyclically orientable graphs
On Deeply Critical Oriented Graphs
, 2001
"... . For every positive integer k, we present an oriented graph G k such that deleting any vertex of G k decreases its oriented chromatic number by at least k and deleting any arc decreases the oriented chromatic number of G k by two. Keywords. Oriented colorings, Critical graphs. 1 ..."
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Cited by 3 (1 self)
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. For every positive integer k, we present an oriented graph G k such that deleting any vertex of G k decreases its oriented chromatic number by at least k and deleting any arc decreases the oriented chromatic number of G k by two. Keywords. Oriented colorings, Critical graphs. 1
SIMPLE SCORE SEQUENCES IN ORIENTED GRAPHS
"... Abstract. We characterize irreducible score sequences of oriented graphs and give a condition for a score sequence to belong to exactly one oriented graph. AMS Mathematics Subject Classification (2000): 05C Key words and phrases: oriented graphs, score sequences ..."
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Abstract. We characterize irreducible score sequences of oriented graphs and give a condition for a score sequence to belong to exactly one oriented graph. AMS Mathematics Subject Classification (2000): 05C Key words and phrases: oriented graphs, score sequences
Competitive colorings of oriented graphs
 Electron J Combina
"... Neˇsetˇril and Sopena introduced a concept of oriented game chromatic number and developed a general technique for bounding this parameter. In this paper, we combine their technique with concepts introduced by several authors in a series of papers on game chromatic number to show that for every posi ..."
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Cited by 10 (3 self)
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positive integer k, there exists an integer t so that if C is a topologically closed class of graphs and C does not contain a complete graph on k vertices, then whenever G is an orientation of a graph from C, the oriented game chromatic number of G is at most t. In particular, oriented planar graphs have
Skew Spectra of Oriented Graphs
"... An oriented graph G σ is a simple undirected graph G with an orientation σ, which assigns to each edge a direction so that G σ becomes a directed graph. G is called the underlying graph of G σ, and we denote by Sp(G) the adjacency spectrum of G. Skewadjacency matrix S(G σ) of G σ is introduced, and ..."
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Cited by 7 (0 self)
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An oriented graph G σ is a simple undirected graph G with an orientation σ, which assigns to each edge a direction so that G σ becomes a directed graph. G is called the underlying graph of G σ, and we denote by Sp(G) the adjacency spectrum of G. Skewadjacency matrix S(G σ) of G σ is introduced
Results 1  10
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432,830