Results 101 to 110 of about 467 (123)
Improved Bounds for the Excluded-Minor Approximation of Treedepth [PDF]
SIAM Journal on Discrete Mathematics, 2021 Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for every positive integers $a,b$ and a graph $G$, if the treedepth of $G$ is at least $Cab$, then the treewidth of $G$ is at least $a$ or $G$ contains a subcubic (
Marcin Pilipczuk +2 more
exaly +11 more sources
Treedepth vs Circumference [PDF]
Combinatorica, 2023 The circumference of a graph $G$ is the length of a longest cycle in $G$, or $+\infty$ if $G$ has no cycle. Birmelé (2003) showed that the treewidth of a graph $G$ is at most its circumference minus $1$. We strengthen this result for $2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth is at most its circumference.
Piotr Micek +2 more
exaly +10 more sources
On the Lossy Kernelization for Connected Treedepth Deletion Set
Lecture Notes in Computer Science, 2022 We study the CONNECTED η -TREEDEPTH DELETION problem, where the input instance is an undirected graph G, and an integer k and the objective is to decide whether there is a vertex set S⊆V(G) such that |S|≤k, every connected component of G−S has treedepth ...
Ramanujan Maadapuzhi Sridharan +2 more
exaly +3 more sources
Integer Programming and Incidence Treedepth [PDF]
Lecture Notes in Computer Science, 2019 Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming is fixed-parameter tractable with respect to the primal (or dual) treedepth of the Gaifman graph of its ...
Michał Pilipczuk +2 more
exaly +8 more sources
Distributed Model Checking on Graphs of Bounded Treedepth [PDF]
AlgorithmicaAbstract We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the model. To our knowledge, this marks the first meta-theorem regarding distributed model checking. Various optimization problems on graphs are expressible
Pedro Montealegre +2 more
exaly +11 more sources
Approximation Algorithms for Treewidth, Pathwidth, and Treedepth—A Short Survey
Lecture Notes in Computer ScienceThis short survey discusses old and new approximation algorithms for treewidth, and for the related parameters pathwidth and treedepth.
Hans Bodlaender
exaly +5 more sources
A graph searching game for block treedepth and a cubic kernel by vertex cover
Theoretical Computer SciencezbMATH Open Web Interface contents unavailable due to conflicting licenses.
Archontia C Giannopoulou +1 more
exaly +7 more sources
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 ...
Marcin Pilipczuk +2 more
exaly +6 more sources
Tight Bound on Treedepth in Terms of Pathwidth and Longest Path [PDF]
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.
Marcin Pilipczuk +2 more
exaly +7 more sources