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Generating Weakly Triangulated Graphs
 Graphs and Combinatorics
, 1993
"... . We show that a graph is weakly triangulated, or weakly chordal, if and only if it can be generated by starting with a graph with no edges, and repeatedly adding an edge, so that the new edge is not the middle edge of any chordless path with four vertices. This is a corollary of results due to Srit ..."
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Cited by 106 (15 self)
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. We show that a graph is weakly triangulated, or weakly chordal, if and only if it can be generated by starting with a graph with no edges, and repeatedly adding an edge, so that the new edge is not the middle edge of any chordless path with four vertices. This is a corollary of results due
Optimizing Slightly Triangulated Graphs
, 1997
"... A graph is called slightly triangulated if it contains no chordless cycle with five or more vertices and every induced subgraph has a vertex whose neighbourhood contains no induced path on four vertices. These graphs generalize triangulated graphs and appear naturally in the study of the intersectio ..."
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A graph is called slightly triangulated if it contains no chordless cycle with five or more vertices and every induced subgraph has a vertex whose neighbourhood contains no induced path on four vertices. These graphs generalize triangulated graphs and appear naturally in the study
Slightly Triangulated Graphs Are Perfect
, 1995
"... A graph is triangulated if it has no chordless cycle with at least four vertices (8k 4; C k 6` G). These graphs have been generalized by R. Hayward with the weakly triangulated graphs (8k 5; C k ; ¯ C k 6` G). In this note we propose a new generalization of triangulated graphs. A graph G is sligh ..."
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Cited by 1 (0 self)
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A graph is triangulated if it has no chordless cycle with at least four vertices (8k 4; C k 6` G). These graphs have been generalized by R. Hayward with the weakly triangulated graphs (8k 5; C k ; ¯ C k 6` G). In this note we propose a new generalization of triangulated graphs. A graph G
Triangulated and Weakly Triangulated Graphs: Simpliciality in Vertices and Edges
, 2001
"... We extend Dirac's characterization by the minimal separators of a triangulated graph to a new characterization for weakly triangulated graphs, and use this to interpret the known properties of weakly triangulated graphs as an extension of the corresponding properties of triangulated graphs. Our ..."
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Cited by 8 (6 self)
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We extend Dirac's characterization by the minimal separators of a triangulated graph to a new characterization for weakly triangulated graphs, and use this to interpret the known properties of weakly triangulated graphs as an extension of the corresponding properties of triangulated graphs
A Generalization of Slightly Triangulated Graphs
, 1999
"... ... In this paper, we introduce a wider class of graphs, obtained by relaxing the neighbourhood condition. We also provide polynomial algorithms to recognize and to produce an optimal coloring of a subclass of slightly triangulated graphs. ..."
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... In this paper, we introduce a wider class of graphs, obtained by relaxing the neighbourhood condition. We also provide polynomial algorithms to recognize and to produce an optimal coloring of a subclass of slightly triangulated graphs.
WingTriangulated Graphs are Perfect
, 1996
"... The winggraph W (G) of a graph G has all edges of G as its vertices; two edges of G are adjacent in W (G) if they are the nonincident edges (called wings) of an induced path on four vertices in G. Ho`ang conjectured that if W (G) has no induced cycle of odd length at least five, then G is perfec ..."
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Cited by 3 (1 self)
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The winggraph W (G) of a graph G has all edges of G as its vertices; two edges of G are adjacent in W (G) if they are the nonincident edges (called wings) of an induced path on four vertices in G. Ho`ang conjectured that if W (G) has no induced cycle of odd length at least five, then G
Monochromatic Paths and Triangulated Graphs
, 1995
"... This paper considers two properties of graphs, one geometrical and one topological, and shows that they are strongly related. Let G be a graph with four distinguished and distinct vertices, w 1 ; w 2 ; b 1 ; b 2 . Consider the two properties, TRI + (G) and MONO(G), defined as follows. TRI + ..."
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This paper considers two properties of graphs, one geometrical and one topological, and shows that they are strongly related. Let G be a graph with four distinguished and distinct vertices, w 1 ; w 2 ; b 1 ; b 2 . Consider the two properties, TRI + (G) and MONO(G), defined as follows. TRI
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
A linear algorithm to color itriangulated graphs
 Information Processing Letters 70, No.2
, 1999
"... Abstract: We show that itriangulated graphs can be colored in linear time by applying lexicographic breadthfirst search (abbreviated LexBFS) and the greedy coloring algorithm. ..."
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Cited by 5 (2 self)
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Abstract: We show that itriangulated graphs can be colored in linear time by applying lexicographic breadthfirst search (abbreviated LexBFS) and the greedy coloring algorithm.
Meyniel Weakly Triangulated Graphs I: Coperfect orderability
 DISCRETE APPL. MATH
, 1997
"... We show that Meyniel weakly triangulated graphs are coperfectly orderable (equivalently, that P 5 free weakly triangulated graphs are perfectly orderable). Our proof is algorithmic, and relies on a notion concerning separating sets, a property of weakly triangulated graphs, and several properties ..."
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Cited by 11 (0 self)
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We show that Meyniel weakly triangulated graphs are coperfectly orderable (equivalently, that P 5 free weakly triangulated graphs are perfectly orderable). Our proof is algorithmic, and relies on a notion concerning separating sets, a property of weakly triangulated graphs, and several properties
Results 1  10
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47,423