Results 101 to 110 of about 4,776 (247)
Size‐Ramsey numbers of graphs with maximum degree three
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract The size‐Ramsey number r̂(H)$\hat{r}(H)$ of a graph H$H$ is the smallest number of edges a (host) graph G$G$ can have, such that for any red/blue colouring of G$G$, there is a monochromatic copy of H$H$ in G$G$. Recently, Conlon, Nenadov and Trujić showed that if H$H$ is a graph on n$n$ vertices and maximum degree three, then r̂(H)=O(n8/5 ...
Nemanja Draganić, Kalina Petrova
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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
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Journal of Graph Theory, Volume 106, Issue 4, Page 816-842, August 2024.Abstract A minimal separator of a graph G is a set S ⊆ V ( G ) such that there exist vertices a , b ∈ V ( G ) ⧹ S with the property that S separates a from b in G, but no proper subset of S does. For an integer k ≥ 0, we say that a minimal separator is k‐simplicial if it can be covered by k cliques and denote by G k the class of all graphs in which ...
Martin Milanič +3 more
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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
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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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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
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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
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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
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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
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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