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Extending Partial Representations of Subclasses of Chordal Graphs
, 2013
"... Chordal graphs are intersection graphs of subtrees of a tree T.We investigate the complexity of the partial representation extension problem for chordal graphs. A partial representation specifies a tree T ′ and some predrawn subtrees of T ′. It asks whether it is possible to construct a representat ..."
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Cited by 7 (3 self)
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Chordal graphs are intersection graphs of subtrees of a tree T.We investigate the complexity of the partial representation extension problem for chordal graphs. A partial representation specifies a tree T ′ and some predrawn subtrees of T ′. It asks whether it is possible to construct a
Strictly chordal graphs and . . .
, 2005
"... A phylogeny is the evolutionary history for a set of evolutionarily related species. The development of hereditary trees, or phylogenetic trees, is an important research subject in computational biology. One development approach, motivated by graph theory, constructs a relationship graph based on ev ..."
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. In this thesis, we give a polynomial time algorithm to solve this problem for strictly chordal graphs, a particular subclass of chordal graphs. During the construction of a solution, we examine the problem for tree chordal graphs, and establish new properties for strictly chordal graphs.
Chordal Probe Graphs (Extended Abstract)
"... In this paper, we introduce the class of chordal probe graphs which are a generalization of both interval probe graphs and chordal graphs. A graph G is chordal probe if its vertices can be partitioned into two sets P (probes) and N (nonprobes) where N is a stable set and such that G can be extended ..."
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Cited by 2 (2 self)
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be extended to a chordal graph by adding edges between nonprobes. We show that a chordal probe graph may contain neither an oddlength chordless cycle nor the complement of a chordless cycle, and we present the complete heirarchy with separating examples for these classes. We give polynomial time recognition
Understanding FaultTolerant Distributed Systems
 COMMUNICATIONS OF THE ACM
, 1993
"... We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design ..."
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Cited by 374 (23 self)
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We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design alternatives, we discuss their relative merits and we give examples of systems which adopt one approach or the other. The aim is to introduce some order in the complex discipline of designing and understanding faulttolerant distributed systems.
Complexity of Generalized Colourings of Chordal Graphs
, 2008
"... The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of graphs P1,...,Pk (usually describing some common graph properties), is to decide, for a given graph G, whether the vertex set of G can be partitioned into sets V1,...,Vk such that, for each i, the induced subg ..."
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Cited by 2 (0 self)
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subgraph of G on Vi belongs to Pi. It can be seen that GCOL generalizes many natural colouring and partitioning problems on graphs. In this thesis, we focus on generalized colouring problems in chordal graphs. The structure of chordal graphs is known to allow solving many difficult combinatorial problems
THE LEAFAGE OF A CHORDAL GRAPH
, 1998
"... The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on nvertex graphs is n − lg n − 1 2 lg lg n + O(1). The proper ..."
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Cited by 1 (0 self)
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The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on nvertex graphs is n − lg n − 1 2 lg lg n + O(1). The proper
Chordal digraphs∗
"... Chordal graphs, also called triangulated graphs, are important in algorithmic graph theory. In this paper we generalise the definition of chordal graphs to the class of directed graphs. Several structural properties of chordal graphs that are crucial for algorithmic applications carry over to the di ..."
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Chordal graphs, also called triangulated graphs, are important in algorithmic graph theory. In this paper we generalise the definition of chordal graphs to the class of directed graphs. Several structural properties of chordal graphs that are crucial for algorithmic applications carry over
Results 1  10
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284,372