Results 11 to 20 of about 4,791 (239)
Chordal Graphs, Even‐Hole‐Free Graphs and Sparse Obstructions to Bounded Treewidth
Journal of Graph Theory, Volume 110, Issue 3, Page 351-365, November 2025.Even‐hole‐free graphs pose a central challenge in identifying hereditary classes of bounded treewidth. We investigate this matter by presenting and studying the following conjecture: for an integer t ≥ 4 and a graph H , every even‐hole‐free graph of ...
Sepehr Hajebi
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2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023 We present a data structure that for a dynamic graph G that is updated by edge insertions and deletions, maintains a tree decomposition of G of width at most $6 k+5$ under the promise that the treewidth of G never grows above k. The amortized update time
T. Korhonen +4 more
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Embedding phylogenetic trees in networks of low treewidth [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic inference methods ...
Leo van Iersel +2 more
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Tight Algorithms for Connectivity Problems Parameterized by Modular-Treewidth [PDF]
International Workshop on Graph-Theoretic Concepts in Computer Science, 2023 We study connectivity problems from a fine-grained parameterized perspective. Cygan et al. (TALG 2022) obtained algorithms with single-exponential running time $\alpha^{tw} n^{O(1)}$ for connectivity problems parameterized by treewidth ($tw$) by ...
Falko Hegerfeld, Stefan Kratsch
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Product structure of graph classes with bounded treewidth [PDF]
Combinatorics, probability & computing, 2022 We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph.
Rutger Campbell +10 more
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Planar Disjoint Paths, Treewidth, and Kernels [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2023 In the PLANAR DISJOINT PATHS problem, one is given an undirected planar graph with a set of k vertex pairs $\left(s_{i}, t_{i}\right)$ and the task is to find k pairwise vertex-disjoint paths such that the i-th path connects $s_{i}$ to $t_{i}$.
Michał Włodarczyk, Meirav Zehavi
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Treewidth versus clique number. II. Tree-independence number [PDF]
J. Comb. Theory B, 2023 Clément Dallard +2 more
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Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
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A Single-Exponential Time 2-Approximation Algorithm for Treewidth [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2021 We give an algorithm, that given an n-vertex graph $G$ and an integer k, in time 2O(k)n either outputs a tree decomposition of $G$ of width at most 2k + 1 or determines that the treewidth of $G$ is larger than k.
T. Korhonen
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Constant Congestion Brambles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 A bramble in an undirected graph $G$ is a family of connected subgraphs of $G$ such that for every two subgraphs $H_1$ and $H_2$ in the bramble either $V(H_1) \cap V(H_2) \neq \emptyset$ or there is an edge of $G$ with one endpoint in $V(H_1)$ and the ...
Meike Hatzel +3 more
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