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112
The cliqueseparator graph for chordal graphs
, 2007
"... We present a new representation of a chordal graph called the cliqueseparator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the cliqueseparator graph and additional properties when the chordal graph is an interval graph, ..."
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Cited by 3 (0 self)
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We present a new representation of a chordal graph called the cliqueseparator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the cliqueseparator graph and additional properties when the chordal graph is an interval graph
Galois groups of chromatic polynomials of strongly noncliqueseparable graphs of order at most 10
, 2009
"... ..."
Chromatic Factorisations
, 2008
"... The chromatic polynomial gives the number of proper λcolourings of a graph G. This paper considers factorisation of the chromatic polynomial as a first step in an algebraic study of the roots of this polynomial. The chromatic polynomial of a graph is said to have a chromatic factorisation if P (G, ..."
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, λ) = P (H1, λ)P (H2, λ)/P (Kr, λ) for some graphs H1 and H2 and clique Kr. It is known that the chromatic polynomial of any cliqueseparable graph, that is, a graph containing a separating rclique, has a chromatic factorisation. We show that there exist other chromatic polynomials that have
Certificates of factorisation for chromatic polynomials
 Electron. J. Combin
"... The chromatic polynomial gives the number of proper λcolourings of a graph G. This paper considers factorisation of the chromatic polynomial as a first step in an algebraic study of the roots of this polynomial. The chromatic polynomial of a graph is said to have a chromatic factorisation if P(G,λ) ..."
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Cited by 2 (2 self)
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(G,λ) = P(H1,λ)P(H2,λ)/P(Kr,λ) for some graphs H1 and H2 and clique Kr. It is known that the chromatic polynomial of any cliqueseparable graph, that is, a graph containing a separating rclique, has a chromatic factorisation. We show that there exist other chromatic polynomials that have chromatic
Chromatic Factors
, 2009
"... The chromatic polynomial P (G, λ) gives the number of proper colourings of a graph G in at most λ colours. If P (G, λ) = P (H1, λ)P (H2, λ) /P (Kr, λ), then G is said to have a chromatic factorisation of order r with chromatic factors H1 and H2. It is clear that, if 0 ≤ r ≤ 2, any H1 ̸ ∼ = Kr wit ..."
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Cited by 2 (0 self)
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certificate for chromatic factorisations of cliqueseparable graphs. 1
Decomposition By Clique Minimal Separators
 Res. Rep. 97213
, 1999
"... Clique decomposition consists in repeatedly finding a clique, the removal of which leaves the graph disconnected, and copying this clique into each of the connected components thus defined. This was implemented efficiently by Tarjan in 1985, and is an important tool for a Divide and Conquer appr ..."
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Cited by 2 (2 self)
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approach to many hard graph problems, as it splits the graph into smaller subgraphs, while preserving holes and antiholes. We define a new sort of decomposition, which uses at each step only clique separators that are also minimal separators of the graph, and has the additional property of being
Register allocation via clique separators
 In Proceedings of the SIGPLAN '89 Conference on Programming Language Design and Implementation
, 1989
"... Abstract Although graph coloring is widely recognized as an effective technique for global register allocation, the overhead can be quite high, not only in execution time but also in memory, as the size of the interference graph needed in coloring can become quite large. In this paper, we present a ..."
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Cited by 35 (4 self)
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an algorithm based upon a result by R. Tarjan regarding the colorability of graphs which are decomposable using clique separators, that improves on the overhead of coloring. The algorithm first partitions program code into code segments using the notion of clique separators. The interference graphs
On clique separators, nearly chordal graphs, and the Maximum Weight Stable Set Problem
, 2004
"... Clique separators in graphs are a helpful tool used by Tarjan as a divideandconquer approach for solving various graph problems such as the Maximum Weight Stable Set (MWS) Problem, Maximum Clique, Graph Coloring and Minimum Fillin but few examples of graph classes having clique separators are know ..."
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Cited by 6 (2 self)
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Clique separators in graphs are a helpful tool used by Tarjan as a divideandconquer approach for solving various graph problems such as the Maximum Weight Stable Set (MWS) Problem, Maximum Clique, Graph Coloring and Minimum Fillin but few examples of graph classes having clique separators
Fast Parallel Algorithms for the Clique Separator Decomposition
, 1990
"... We give an efficient NC algorithm for finding a clique separator decomposition of an arbitrary graph, that is, a series of cliques whose removal disconnects the graph. This algorithm allows one to extend a large body of results which were originally formulated for chordal graphs to other classes of ..."
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Cited by 4 (1 self)
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We give an efficient NC algorithm for finding a clique separator decomposition of an arbitrary graph, that is, a series of cliques whose removal disconnects the graph. This algorithm allows one to extend a large body of results which were originally formulated for chordal graphs to other classes
Results 1  10
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112