Results 91 to 100 of about 11,780 (248)
Super stable tensegrities and the Colin de Verdière number ν
Journal of Graph Theory, Volume 108, Issue 3, Page 401-431, March 2025.Abstract A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars and struts connected by cables with tension. We introduce the super stability number of a multigraph as the maximum dimension that a multigraph can be realized as a super stable tensegrity, and show that it equals the Colin de ...
Ryoshun Oba, Shin‐ichi Tanigawa
wiley +1 more source
An Improved Parameterized Algorithm for Treewidth
SIAM Journal on Computing, 2023 57 pages, 2 figures. STOC 2023.
Tuukka Korhonen, Daniel Lokshtanov
openaire +2 more sources
Size‐Ramsey numbers of graphs with maximum degree three
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract The size‐Ramsey number r̂(H)$\hat{r}(H)$ of a graph H$H$ is the smallest number of edges a (host) graph G$G$ can have, such that for any red/blue colouring of G$G$, there is a monochromatic copy of H$H$ in G$G$. Recently, Conlon, Nenadov and Trujić showed that if H$H$ is a graph on n$n$ vertices and maximum degree three, then r̂(H)=O(n8/5 ...
Nemanja Draganić, Kalina Petrova
wiley +1 more source
Graph limits of random graphs from a subset of connected k‐trees
Random Structures &Algorithms, Volume 55, Issue 1, Page 125-152, August 2019., 2019 For any set Ω of non‐negative integers such that , we consider a random Ω‐k‐tree Gn,k that is uniformly selected from all connected k‐trees of (n + k) vertices such that the number of (k + 1)‐cliques that contain any fixed k‐clique belongs to Ω. We prove that Gn,k, scaled by where Hk is the kth harmonic number and σΩ > 0, converges to the continuum ...
Michael Drmota +2 more
wiley +1 more source
Treewidth Lower Bounds with Brambles [PDF]
Algorithmica, 2005 In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph g is the maximum order of a bramble of g minus one. We give two algorithms: one for general graphs, and one for planar graphs.
Alexander Grigoriev +2 more
openaire +6 more sources
TREEWIDTH and PATHWIDTH parameterized by vertex cover
, 2013 After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to the Vertex Cover.
Chapelle, Mathieu +3 more
core +3 more sources
The Parameterised Complexity of List Problems on Graphs of Bounded Treewidth [PDF]
, 2016 We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable, parameterised by ...
Meeks, Kitty, Scott, Alexander
core +2 more sources
Journal of Graph Theory, Volume 106, Issue 4, Page 816-842, August 2024.Abstract A minimal separator of a graph G is a set S ⊆ V ( G ) such that there exist vertices a , b ∈ V ( G ) ⧹ S with the property that S separates a from b in G, but no proper subset of S does. For an integer k ≥ 0, we say that a minimal separator is k‐simplicial if it can be covered by k cliques and denote by G k the class of all graphs in which ...
Martin Milanič +3 more
wiley +1 more source
On the treewidth of triangulated 3-manifolds [PDF]
Journal of Computational Geometry, 2017 In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is ...
Huszár, Kristóf +2 more
openaire +6 more sources
Subcubic graphs of large treewidth do not have the edge-Erdős-Pósa property [PDF]
arXiv, 2023 We show that subcubic graphs of treewidth at least $2500$ do not have the edge-Erd\H{o}s-P\'{o}sa property.
arxiv