Results 1  10
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2,658
Testing Superperfection of ktrees
, 1992
"... An interval coloring of a weighted graph with nonnegative weights, maps each vertex onto an open interval on the real line with width equal to the weight of the vertex, such that adjacent vertices are mapped to disjoint intervals. The total ..."
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An interval coloring of a weighted graph with nonnegative weights, maps each vertex onto an open interval on the real line with width equal to the weight of the vertex, such that adjacent vertices are mapped to disjoint intervals. The total
Counting HColorings of Partial kTrees
"... The problem of counting all Hcolorings of a graph G with n vertices is considered. While the problem is, in general, #Pcomplete, we give linear time algorithms that solve the main variants of this problem when the input graph G is a ktree or, in the case where G is directed, when the underlying g ..."
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Cited by 14 (3 self)
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graph of G is a ktree. Our algorithms remain polynomial even in the case where k = O(log n) or in the case where the size of H is O(n). Our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial ktrees such as core checking and chromatic
A Partial KArboretum of Graphs With Bounded Treewidth
 J. Algorithms
, 1998
"... The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes ..."
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Cited by 328 (34 self)
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The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between
Partitioning the edges of a planar graph into two partial ktrees
 In Proc. 19th Southeastern Conf. on Combinatorics, Graph Theory, and Computing
, 1988
"... In this paper we prove two results on partitioning the edges of a planar graph into two partial ktrees, for fixed values of k. Interest in this class of partitioning problems arises since many intractable graph and network problems admit polynomial time solutions on ktrees and their subgraphs (par ..."
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Cited by 5 (0 self)
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In this paper we prove two results on partitioning the edges of a planar graph into two partial ktrees, for fixed values of k. Interest in this class of partitioning problems arises since many intractable graph and network problems admit polynomial time solutions on ktrees and their subgraphs
Partitioning Problems: Characterization, Complexity and Algorithms on Partial kTrees
, 1994
"... This thesis investigates the computational complexity of algorithmic problems defined on graphs. At the abstract level of the complexity spectrum we discriminate polynomialtime solvable problems from N Pcomplete problems, while at the concrete level we improve on polynomialtime algorithms for gen ..."
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Cited by 8 (1 self)
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This thesis investigates the computational complexity of algorithmic problems defined on graphs. At the abstract level of the complexity spectrum we discriminate polynomialtime solvable problems from N Pcomplete problems, while at the concrete level we improve on polynomialtime algorithms
Treepartitions of ktrees with applications in graph layout
 Proc. 29th Workshop on Graph Theoretic Concepts in Computer Science (WG’03
, 2002
"... Abstract. A treepartition of a graph is a partition of its vertices into ‘bags ’ such that contracting each bag into a single vertex gives a forest. It is proved that every ktree has a treepartition such that each bag induces a (k − 1)tree, amongst other properties. Applications of this result t ..."
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Cited by 13 (11 self)
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Abstract. A treepartition of a graph is a partition of its vertices into ‘bags ’ such that contracting each bag into a single vertex gives a forest. It is proved that every ktree has a treepartition such that each bag induces a (k − 1)tree, amongst other properties. Applications of this result
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
The bchromatic index of a graph
, 2012
"... The bchromatic index ϕ′(G) of a graph G is the largest integer k such that G admits a proper kedge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The bchromatic index of trees is determined and equals either to a natural upper ..."
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Cited by 1 (0 self)
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The bchromatic index ϕ′(G) of a graph G is the largest integer k such that G admits a proper kedge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The bchromatic index of trees is determined and equals either to a natural upper
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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the class of languages decidable by a random expected polynomialtime algorithm that makes no errors. Our result matches (up to low order terms) the known gap for approximating the size of the largest independent set. Previous O(N ffi ) gaps for approximating the chromatic number (such as those by Lund
Results 1  10
of
2,658