Results 51 to 60 of about 2,730 (147)

Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming

Algorithms, 2018
Treedepth is a well-established width measure which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted than graphs of bounded tree- or pathwidth, we are interested in the algorithmic utility of this ...
Li-Hsuan Chen, Felix Reidl, Peter Rossmanith, Fernando Sánchez Villaamil   +3 more
doaj   +1 more source

The treewidth and pathwidth of hypercubes

Discrete Mathematics, 2006
AbstractThe d-dimensional hypercube, Hd, is the graph on 2d vertices, which correspond to the 2d d-vectors whose components are either 0 or 1, two of the vertices being adjacent when they differ in just one coordinate. The notion of Hamming graphs (denoted by Kqd) generalizes the notion of hypercubes: The vertices correspond to the qd d-vectors where ...
L. Sunil Chandran, Telikepalli Kavitha
openaire   +2 more sources

Outerplanar Obstructions for Matroid Pathwidth

Electronic Notes in Discrete Mathematics, 2011
For each non-negative integer k, we provide all outerplanar obstructions for the class of graphs whose cycle matroid has pathwidth at most k. Our proof combines a decomposition lemma for proving lower bounds on matroid pathwidth and a relation between matroid pathwidth and linear width.
Koichi Yamazaki, Dimitrios M. Thilikos, Dimitrios M. Thilikos, Athanassios Koutsonas   +3 more
openaire   +9 more sources

Obstructions to within a few vertices or edges of acyclic [PDF]

, 1995
Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals.
Cattell, Kevin, Dinneen, Michael J., Fellows, Michael R.   +2 more
core   +3 more sources

On Approximating Cutwidth and Pathwidth

2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)
We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $ \log^{1+o(1)}(n)$ approximation for the problem, substantially improving upon the previous poly-logarithmic guarantees based
Bansal, Nikhil, Katzelnick, Dor, Schwartz, Roy   +2 more
openaire   +2 more sources

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, Linda Cook, Meike Hatzel, Claire Hilaire, Freddie Illingworth, Rose McCarty   +5 more
wiley   +1 more source

Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2

, 2018
Deciding whether a given graph has a square root is a classical problem that has been studied extensively both from graph theoretic and from algorithmic perspectives.
A Mukhopadhyay, B Courcelle, B Courcelle, B Farzad, HL Bodlaender, HL Bodlaender, IC Ross, LC Lau, LC Lau, M Cochefert, M Cochefert, M Milanic, M Milanic, MM Sysło, NG Kinnersley, NV Nestoridis, PA Golovach, PA Golovach, R Diestel, R Motwani, VB Le, VB Le, VB Le, VB Le, Y-L Lin   +24 more
core   +1 more source

The product structure of squaregraphs

Journal of Graph Theory, Volume 105, Issue 2, Page 179-191, February 2024.
Abstract A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path.
Robert Hickingbotham, Paul Jungeblut, Laura Merker, David R. Wood   +3 more
wiley   +1 more source

Seymour’s Conjecture on 2-Connected Graphs of Large Pathwidth [PDF]

Combinatorica, 2020
We prove the conjecture of Seymour (1993) that for every apex-forest $H_1$ and outerplanar graph $H_2$ there is an integer $p$ such that every 2-connected graph of pathwidth at least $p$ contains $H_1$ or $H_2$ as a minor. An independent proof was recently obtained by Dang and Thomas.
Huynh T., Joret G., Micek P., Wood D. R.
openaire   +4 more sources

Two Results on Layered Pathwidth and Linear Layouts [PDF]

arXiv, 2020
Layered pathwidth is a new graph parameter studied by Bannister et al (2015). In this paper we present two new results relating layered pathwidth to two types of linear layouts. Our first result shows that, for any graph $G$, the stack number of $G$ is at most four times the layered pathwidth of $G$.
arxiv