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INDEPENDENT SETS IN ASTEROIDAL TRIPLEFREE GRAPHS∗
"... Abstract. An asteroidal triple (AT) is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called ATfree if it does not have an AT. We show that there is an O(n4) time algorithm to compute the maximum weight of an inde ..."
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Abstract. An asteroidal triple (AT) is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called ATfree if it does not have an AT. We show that there is an O(n4) time algorithm to compute the maximum weight
Asteroidal TripleFree Graphs
, 1997
"... . An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triples. The motivation for this investigation was provided, in ..."
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Cited by 61 (9 self)
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. An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triples. The motivation for this investigation was provided
Approximating the Bandwidth for Asteroidal TripleFree Graphs
"... We show that there is an O(n^3) algorithm to approximate the bandwidth of an ATfree graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an O(e + n log n) algorithm to approximate the bandwidth of an ATfree graph within a factor 4 an ..."
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Cited by 35 (1 self)
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We show that there is an O(n^3) algorithm to approximate the bandwidth of an ATfree graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an O(e + n log n) algorithm to approximate the bandwidth of an ATfree graph within a factor 4
Powers of Asteroidal Triplefree Graphs with Applications
"... . An asteroidal triple is an independent set of three vertices in a graph such that every two of them are joined by a path avoiding the closed neighborhood of the third. Graphs without asteroidal triples are called ATfree graphs. In this paper, we show that every ATfree graph admits a vertex o ..."
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Cited by 2 (1 self)
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. An asteroidal triple is an independent set of three vertices in a graph such that every two of them are joined by a path avoiding the closed neighborhood of the third. Graphs without asteroidal triples are called ATfree graphs. In this paper, we show that every ATfree graph admits a vertex
LexBFSordering in Asteroidal Triplefree Graphs
 SpringerVerlag Lecture Notes in Computer Science 1741
, 1999
"... . In this paper, we study the metric property of LexBFSordering on ATfree graphs. Based on a 2sweep LexBFS algorithm, we show that every ATfree graph admits a vertex ordering, called the strong 2cocomparability ordering, that for any three vertices u OE v OE w in the ordering, if d(u; w) 2 ..."
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Cited by 3 (0 self)
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. In this paper, we study the metric property of LexBFSordering on ATfree graphs. Based on a 2sweep LexBFS algorithm, we show that every ATfree graph admits a vertex ordering, called the strong 2cocomparability ordering, that for any three vertices u OE v OE w in the ordering, if d(u; w) 2
Linear Time Algorithms for Dominating Pairs in Asteroidal Triplefree Graphs
 SIAM J. Comput
, 1997
"... An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighbourhood of the third. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triple. The motivation for this work is pro ..."
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Cited by 31 (6 self)
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An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighbourhood of the third. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triple. The motivation for this work
Computing a Dominating Pair in an Asteroidal Triplefree Graph in Linear Time
 in Algorithms and Data Structures WADS '95, Lecture
, 1998
"... An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triple. The motivation for this work is prov ..."
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Cited by 3 (2 self)
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An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triple. The motivation for this work
Efficient Algorithms on Asteroidal TripleFree and Distance Hereditary Graphs
, 1993
"... One way of overcoming the intractable nature of problems in graphs is by considering them on special classes of graphs. In this thesis, we study the properties of two important classes of graphs  asteroidal triplefree graphs and distancehereditary graphs, and use their properties to design effici ..."
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One way of overcoming the intractable nature of problems in graphs is by considering them on special classes of graphs. In this thesis, we study the properties of two important classes of graphs  asteroidal triplefree graphs and distancehereditary graphs, and use their properties to design
Domination and Total Domination on Asteroidal TripleFree Graphs
, 1996
"... We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triplefree graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating ..."
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Cited by 12 (3 self)
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We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triplefree graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
Results 1  10
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