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52,582
Zero Knowledge and the Chromatic Number
 Journal of Computer and System Sciences
, 1996
"... We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number wi ..."
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Cited by 207 (7 self)
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We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number
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 the Hardness of Approximating the Chromatic Number
, 1993
"... We study the hardness of approximating the chromatic number when the input graph is kcolorable for some fixed k 3. Our main result is that it is NPhard to find a 4coloring of a 3chromatic graph. As an immediate corollary we obtain that it is NPhard to color a kchromatic graph with at most ..."
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Cited by 80 (6 self)
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We study the hardness of approximating the chromatic number when the input graph is kcolorable for some fixed k 3. Our main result is that it is NPhard to find a 4coloring of a 3chromatic graph. As an immediate corollary we obtain that it is NPhard to color a kchromatic graph with at most
On the adaptable chromatic number . . .
"... The adaptable chromatic number of a graphG is the smallest integer k such that for any edge kcolouring of G there exists a vertex kcolouring of G in which the same colour never appears on an edge and both its endpoints. (Neither the edge nor the vertex colourings are necessarily proper in the usua ..."
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The adaptable chromatic number of a graphG is the smallest integer k such that for any edge kcolouring of G there exists a vertex kcolouring of G in which the same colour never appears on an edge and both its endpoints. (Neither the edge nor the vertex colourings are necessarily proper
On the Oriented Game Chromatic Number
, 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), 133147]. We prove that every oriented path has oriented game chromatic number at most 7 (and this bound is tight), that every oriented ..."
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Cited by 2 (0 self)
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. 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), 133147]. We prove that every oriented path has oriented game chromatic number at most 7 (and this bound is tight), that every
Game Chromatic Number of Graphs
 Discrete Math
, 1998
"... We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particula ..."
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Cited by 11 (3 self)
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We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs
The Local Chromatic Number
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The local chromatic number ψ(G) of a graph G is a grap ..."
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The local chromatic number ψ(G) of a graph G is a
On the complexity of the circular chromatic number
 J. Graph Theory
, 2004
"... Circular chromatic number, χc is a natural generalization of chromatic number. It is known that it is NPhard to determine whether or not an arbitrary graph G satisfies χ(G) = χc(G). In this paper we prove that this problem is NPhard even if the chromatic number of the graph is known. This answers ..."
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Cited by 2 (1 self)
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Circular chromatic number, χc is a natural generalization of chromatic number. It is known that it is NPhard to determine whether or not an arbitrary graph G satisfies χ(G) = χc(G). In this paper we prove that this problem is NPhard even if the chromatic number of the graph is known
CHROMATIC NUMBERS OF HYPERBOLIC SURFACES
"... Abstract. This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the dchromatic number is the minimum number of colors needed to color the points of the space so that any two points at distance d are of a different color. We prove upper bounds on the dchromatic number ..."
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Abstract. This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the dchromatic number is the minimum number of colors needed to color the points of the space so that any two points at distance d are of a different color. We prove upper bounds on the dchromatic number
Results 1  10
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