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THE SIZE OF CHORDAL, INTERVAL AND THRESHOLD SUBGRAPHS
 COMBINATORICA 9(3)(1989)245253
, 1989
"... Given a graph G with II vertices and m edges, how many edges must be in thelargest chordal subgraph of G? For m=na/4+ 1, the answer is 3n/2 1. For m=na/3, it is 2n3. For m = n2/3 + 1, it is at least 7n/3 6 and at most 8n/3 4. Similar questions are studied, with less complete resuIts, for thresho ..."
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Cited by 1 (0 self)
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Given a graph G with II vertices and m edges, how many edges must be in thelargest chordal subgraph of G? For m=na/4+ 1, the answer is 3n/2 1. For m=na/3, it is 2n3. For m = n2/3 + 1, it is at least 7n/3 6 and at most 8n/3 4. Similar questions are studied, with less complete resu
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 such classes are discussed.
Distance Approximating Trees for Chordal and Dually Chordal Graphs
, 1999
"... In this paper we show that, for each chordal graph G, there is a tree T such that T is a spanning tree of the square G² of G and, for every two vertices, the distance between them in T is not larger than the distance in G plus 2. Moreover, we prove that, if G is a strongly chordal graph or even a ..."
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Cited by 31 (18 self)
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In this paper we show that, for each chordal graph G, there is a tree T such that T is a spanning tree of the square G² of G and, for every two vertices, the distance between them in T is not larger than the distance in G plus 2. Moreover, we prove that, if G is a strongly chordal graph or even
On Powers of Chordal Graphs And Their Colorings
 Congr. Numer
, 2000
"... The kth power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs of t ..."
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Cited by 24 (1 self)
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of the known facts that any power of an interval graph is an interval graph, and that any odd power of a general chordal graph is again chordal. We then show that it is computationally hard to approximately color the even powers of n vertex chordal graphs within an n 1 2 \Gammaffl factor, for any ffl
Fully dynamic algorithms for chordal graphs
, 2001
"... We present the first dynamic algorithm that maintains a clique tree representation of a chordal graph and supports the following operations: (1) query whether deleting or inserting an arbitrary edge preserves chordality, (2) delete or insert an arbitrary edge, provided it preserves chordality. We gi ..."
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Cited by 35 (2 self)
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We present the first dynamic algorithm that maintains a clique tree representation of a chordal graph and supports the following operations: (1) query whether deleting or inserting an arbitrary edge preserves chordality, (2) delete or insert an arbitrary edge, provided it preserves chordality. We
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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to the directed setting, including notions like simplicial vertices, perfect elimination orderings, and characterisation by forbidden subgraphs resembling chordless cycles. Moreover, just as chordal graphs are related to treewidth, the chordal digraphs will be related to Kellywidth. 1
Branchwidth of chordal graphs
, 2007
"... This paper revisits the ’branchwidth territories’ of Kloks, Kratochvíl and Müller [12] to provide a simpler proof and a faster algorithm for computing branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running time ..."
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This paper revisits the ’branchwidth territories’ of Kloks, Kratochvíl and Müller [12] to provide a simpler proof and a faster algorithm for computing branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running
Results 1  10
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2,707