Results 1 to 10 of about 2,459 (116)

Structural parameterizations for boxicity [PDF]

, 2014
The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d ...
A Adiga, A Adiga, A Adiga, A Adiga, A Bielecki, B Courcelle, C Thomassen, E Asplund, FS Roberts, HL Bodlaender, J Kratochvíl, J Spinrad, L Cai, LS Chandran, M Doucha, M Yannakakis, MR Fellows, R Diestel, R Ganian, RG Downey   +19 more
core   +1 more source

On the Geometric Ramsey Number of Outerplanar Graphs

, 2013
We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on $2n$ vertices are bounded by $O(n^{3})$ and $O(
Cibulka, Josef, Gao, Pu, Krčál, Marek, Valla, Tomáš, Valtr, Pavel   +4 more
core   +1 more source

A General Reduction Theorem with Applications to Pathwidth and the Complexity of MAX 2-CSP [PDF]

, 2015
We prove a general reduction theorem which allows us to extend bounds for certain graph parameters on cubic graphs to bounds for general graphs taking into account the individual vertex degrees.
A Golovnev, AD Scott, AD Scott, Eric McDermid, F Della Croce, FV Fomin, FV Fomin, FV Fomin, GJ Woeginger, HL Bodlaender, J Gramm, J Kneis, Keith Edwards, KJ Edwards, KJ Edwards, P Haxell, R Niedermeier, S Arnborg, S Gaspers   +18 more
core   +3 more sources

LTL Fragments are Hard for Standard Parameterisations

, 2015
We classify the complexity of the LTL satisfiability and model checking problems for several standard parameterisations. The investigated parameters are temporal depth, number of propositional variables and formula treewidth, resp., pathwidth.
Lück, Martin, Meier, Arne
core   +1 more source

A Tight Lower Bound for Counting Hamiltonian Cycles via Matrix Rank [PDF]

, 2017
For even $k$, the matchings connectivity matrix $\mathbf{M}_k$ encodes which pairs of perfect matchings on $k$ vertices form a single cycle. Cygan et al.
Curticapean, Radu, Lindzey, Nathan, Nederlof, Jesper   +2 more
core   +3 more sources

The Effect of Planarization on Width

, 2017
We study the effects of planarization (the construction of a planar diagram $D$ from a non-planar graph $G$ by replacing each crossing by a new vertex) on graph width parameters.
DG Corneil, DJ Kleitman, F Gurski, FRK Chung, G Battista Di, G Borradaile, H Edelsbrunner, J Nešetřil, K Thulasiraman, K Zarankiewicz, NG Kinnersley, NV Nestoridis, PD Seymour, R Cimikowski, S Garfunkel   +14 more
core   +1 more source

Circumference and Pathwidth of Highly Connected Graphs [PDF]

, 2014
Birmele [J. Graph Theory, 2003] proved that every graph with circumference t has treewidth at most t-1. Under the additional assumption of 2-connectivity, such graphs have bounded pathwidth, which is a qualitatively stronger result. Birmele's theorem was
Marshall, Emily A., Wood, David R.
core   +1 more source

Simple Counting and Sampling Algorithms for Graphs with Bounded Pathwidth [PDF]

, 2022
Christine T. Cheng, Will Rosenbaum
openalex   +1 more source

The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations

Algorithms
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width
Frank Gurski, Robin Weishaupt
doaj   +1 more source

$n$-permutability and linear Datalog implies symmetric Datalog

, 2018
We show that if $\mathbb A$ is a core relational structure such that CSP($\mathbb A$) can be solved by a linear Datalog program, and $\mathbb A$ is $n$-permutable for some $n$, then CSP($\mathbb A$) can be solved by a symmetric Datalog program (and thus ...
Kazda, Alexandr
core   +1 more source