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Polynomial Treedepth Bounds in Linear Colorings [PDF]
Algorithmica, 2020 AbstractLow-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former ...
Jeremy Kun +2 more
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Exploring the Gap Between Treedepth and Vertex Cover Through Vertex Integrity [PDF]
Lecture Notes in Computer Science, 2021 30 pages, 5 figures, CIAC ...
Tatsuya Gima +2 more
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Tight Bound on Treedepth in Terms of Pathwidth and Longest Path
Combinatorica, 2023 We show that every graph with pathwidth strictly less than $a$ that contains no path on $2^b$ vertices as a subgraph has treedepth at most $10ab$. The bound is best possible up to a constant factor.
Gwenaël Joret, Bartosz Walczak
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MaxSAT-Based Postprocessing for Treedepth
Lecture Notes in Computer Science, 2020Treedepth is an increasingly popular graph invariant. Many NP-hard combinatorial problems can be solved efficiently on graphs of bounded treedepth. Since the exact computation of treedepth is itself NP-hard, recent research has focused on the development of heuristics that compute good upper bounds on the treedepth.
Vaidyanathan P R, Stefan Szeider
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On the Lossy Kernelization for Connected Treedepth Deletion Set
Lecture Notes in Computer Science, 2022Eduard Eiben +2 more
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Treedepth Bounds in Linear Colorings
Lecture Notes in Computer Science, 2018Low-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former dominates ...
Jeremy Kun +2 more
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On the size of minimal separators for treedepth decomposition
Discrete Applied MathematicsThe major changes from the first version are as follows. (1) The conjecture was resolved and the upper bound was slightly improved. (2) The experimental results were not correct and were removed. Specifically, there was a problem in the separator enumeration when we extended SMS [Korhonen 2020].
Vorapong Suppakitpaisarn
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Compact representation of graphs with bounded bandwidth or treedepth
Information and Computation, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shahin Kamali
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A Heuristic Approach to the Treedepth Decomposition Problem for Large Graphs
Lecture Notes in Computer Science, 2021In this article, we describe algorithms and techniques used in the method ExTREEm for the treedepth decomposition problem. ExTREEm won the heuristic track of the 5th Parameterized Algorithms and Computational Experiments Challenge (PACE 2020). It searches for a minimum-height treedepth decomposition of a graph via computing graph separators.
Sylwester Swat, Marta Kasprzak
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Compact Representation of Graphs with Small Bandwidth and Treedepth
2020 Data Compression Conference (DCC), 2020We consider the problem of compact representation of graphs with small bandwidth as well as graphs with small treedepth. These parameters capture structural properties of graphs that come in useful in certain applications. We present simple navigation oracles that support degree and adjacency queries in constant time and neighborhood query in constant ...
Shahin Kamali
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