Results 121 to 130 of about 13,679 (262)
Tree independence number I. (Even hole, diamond, pyramid)‐free graphs
Journal of Graph Theory, Volume 106, Issue 4, Page 923-943, August 2024.Abstract The tree‐independence number tree‐ α, first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. developed the so‐called central bag method to study induced obstructions to bounded treewidth.
Tara Abrishami +5 more
wiley +1 more source
Discrete Mathematics, 2006 AbstractA set of vertices S⊆V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G-S of the graph, obtained by making S a clique in the subgraph of G, induced by W∪S. We show that such safe separators are a very powerful tool for preprocessing
Hans L. Bodlaender, Arie M. C. A. Koster
openaire +5 more sources
Advances in Learning Bayesian Networks of Bounded Treewidth [PDF]
, 2014 This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed.
de Campos, Cassio Polpo +3 more
core +4 more sources
A more accurate view of the Flat Wall Theorem
Journal of Graph Theory, Volume 107, Issue 2, Page 263-297, October 2024.Abstract We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in flat walls.
Ignasi Sau +2 more
wiley +1 more source
On the parameterized complexity of computing tree-partitions [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree.
Hans L. Bodlaender +2 more
doaj +1 more source
Approximating the Treewidth of AT-Free Graphs
Discrete Applied Mathematics, 2000 AbstractUsing the specific structure of the minimal separators of AT-free graphs, we give a polynomial time algorithm that computes a triangulation whose width is no more than twice the treewidth of the input graph.
Bouchitté, Vincent, Todinca, Ioan
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On the treewidth of triangulated 3-manifolds [PDF]
Journal of Computational Geometry, 2017 In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is ...
Huszár, Kristóf +2 more
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The pathwidth and treewidth of cographs [PDF]
SIAM Journal on Discrete Mathematics, 1990 It is shown that the pathwidth of a cograph equals its treewidth, and a linear time algorithm to determine the pathwidth of a cograph and build a corresponding path-decomposition is given.
Hans L. Bodlaender, Rolf H. Möhring
openaire +2 more sources
Graphs with at most two moplexes
Journal of Graph Theory, Volume 107, Issue 1, Page 38-69, September 2024.Abstract A moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. The notion is known to be closely related to lexicographic searches in graphs as well as to asteroidal triples, and has been applied in several algorithms related to graph classes, such as interval graphs, claw‐free ...
Clément Dallard +4 more
wiley +1 more source
On tree decompositions whose trees are minors
Journal of Graph Theory, Volume 106, Issue 2, Page 296-306, June 2024.Abstract In 2019, Dvořák asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$.
Pablo Blanco +5 more
wiley +1 more source