Results 81 to 90 of about 1,532 (205)
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
, 2005 Treewidth is a graph parameter with several interesting theoretical and practical applications. This survey reviews algorithmic results on determining the treewidth of a given graph, and finding a tree decomposition of small width. Both theoretical results, establishing the asymptotic computational complexity of the problem, as experimental work on ...
openaire +3 more sources
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bodlaender, H.L., Koster, A.M.C.A.
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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
Treewidth Lower Bounds with Brambles [PDF]
Algorithmica, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bodlaender, H.L. +2 more
openaire +5 more sources
Treewidth 2 in the Planar Graph Product Structure Theorem [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any
Marc Distel +4 more
doaj +1 more source
A Strategy for Dynamic Programs: Start over and Muddle through [PDF]
Logical Methods in Computer Science, 2019 In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic.
Samir Datta +4 more
doaj +1 more source
A 2-Approximation for the Bounded Treewidth Sparsest Cut Problem in FPT\n Time [PDF]
, 2021 Vincent Cohen-Addad +2 more
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Induced subgraphs and tree decompositions V. one neighbor in a hole
Journal of Graph Theory, Volume 105, Issue 4, Page 542-561, April 2024.Abstract What are the unavoidable induced subgraphs of graphs with large treewidth? It is well‐known that the answer must include a complete graph, a complete bipartite graph, all subdivisions of a wall and line graphs of all subdivisions of a wall (we refer to these graphs as the “basic treewidth obstructions”).
Tara Abrishami +5 more
wiley +1 more source