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83
Detecting Holes and Antiholes in Graphs
, 2007
"... In this paper we study the problems of detecting holes and antiholes in general undirected graphs, and we present algorithms for these problems. For an input graph G on n vertices and m edges, our algorithms run in O(n + m 2) time and require O(nm) space; we thus provide a solution to the open prob ..."
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Cited by 2 (0 self)
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In this paper we study the problems of detecting holes and antiholes in general undirected graphs, and we present algorithms for these problems. For an input graph G on n vertices and m edges, our algorithms run in O(n + m 2) time and require O(nm) space; we thus provide a solution to the open
Hole and Antihole Detection in Graphs
, 2004
"... In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m²) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad, a ..."
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Cited by 16 (3 self)
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In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m²) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad
Algorithms for square3PC(·, ·)free Berge graphs
, 2006
"... We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and squarefree Berge gr ..."
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Cited by 8 (6 self)
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We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and squarefree Berge
On the Way to Perfection: Primal Operations for Stable Sets in Graphs
"... In this paper some operations are described that transform every graph into a perfect graph by replacing nodes with sets of new nodes. The transformation is done in such a way that every stable set in the perfect graph corresponds to a stable set in the original graph. These operations yield a pure ..."
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that would lead to pivoting into nonintegral basic feasible solutions, are replaced by new columns that one can read o# from special graph structures such as odd holes, odd antiholes, and various generalizations. Eventually, either a pivot leading to an integral basic feasible solution is performed
A Bergekeeping operation for graphs
, 2003
"... The Strong Perfect Graph Theorem is a corollary of decomposition results stating that the undecomposable Berge graphs are very particular perfect graphs. The fantastic monument built up by Chudnovsky, Robertson, Seymour and Thomas modifies the center of interest of the entire field. An interesting o ..."
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and perfect graphs, may survive. It is about a single and simple operation that does not create odd holes or odd antiholes in a graph unless there are already some. In order to apply it we need a vertex whose neighborhood has an optimal coloration where the union of any two color classes is a connected graph
unknown title
"... In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m 2) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad, ..."
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In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m 2) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad
Recognizing Weakly Triangulated Graphs by Edge Separability
, 2000
"... . We apply Lekkerkerker and Boland's recognition algorithm for triangulated graphs to the class of weakly triangulated graphs. This yields a new characterization of weakly triangulated graphs, as well as a new O(m 2 ) recognition algorithm which, unlike the previous ones, is not based on the ..."
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Cited by 27 (12 self)
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. We apply Lekkerkerker and Boland's recognition algorithm for triangulated graphs to the class of weakly triangulated graphs. This yields a new characterization of weakly triangulated graphs, as well as a new O(m 2 ) recognition algorithm which, unlike the previous ones, is not based
Detecting wheels
 Applicable Analysis and Discrete Mathematics
"... A wheel is a graph made of a cycle of length at least 4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph G and whose question is “does G contains a wheel as an induced subgraph ” is NPcomplete. We also settle the complexity o ..."
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Cited by 3 (1 self)
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A wheel is a graph made of a cycle of length at least 4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph G and whose question is “does G contains a wheel as an induced subgraph ” is NPcomplete. We also settle the complexity
Graph Extremities and Minimal Separation
 Proceedings of JIM 2003
, 2003
"... Many problems related to knowledge discovery can be modelized by an undirected graph, which in turn has a strong structure associated with its minimal separators. On several wellknown graph classes which are used in applications, the graph extremities and the related elimination orderings are an ef ..."
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Cited by 2 (1 self)
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Many problems related to knowledge discovery can be modelized by an undirected graph, which in turn has a strong structure associated with its minimal separators. On several wellknown graph classes which are used in applications, the graph extremities and the related elimination orderings
RECOGNIZING PERFECT 2SPLIT GRAPHS
, 2000
"... A graph is a split graph if its vertices can be partitioned into a clique and a stable set. A graph is a ksplit graph if its vertices can be partitioned into k sets, each of which induces a split graph. We show that the strong perfect graph conjecture is true for 2split graphs and we design a poly ..."
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Cited by 4 (0 self)
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A graph is a split graph if its vertices can be partitioned into a clique and a stable set. A graph is a ksplit graph if its vertices can be partitioned into k sets, each of which induces a split graph. We show that the strong perfect graph conjecture is true for 2split graphs and we design a
Results 1  10
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83