Results 111 to 120 of about 13,679 (262)
Mathematics, 2023 Considering the worst-case scenario, the junction-tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees.
Alexander Bauer +2 more
doaj +1 more source
On the dimension of posets with cover graphs of treewidth $2$ [PDF]
, 2016 In 1977, Trotter and Moore proved that a poset has dimension at most $3$ whenever its cover graph is a forest, or equivalently, has treewidth at most $1$.
Joret, Gwenaël +4 more
core +3 more sources
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
Contraction obstructions for treewidth
Journal of Combinatorial Theory, Series B, 2011 AbstractWe provide two parameterized graphs Γk, Πk with the following property: for every positive integer k, there is a constant ck such that every graph G with treewidth at least ck, contains one of Kk, Γk, Πk as a contraction, where Kk is a complete graph on k vertices.
Petr A. Golovach +2 more
openaire +2 more sources
An Experimental Study of the Treewidth of Real-World Graph Data (Extended Version) [PDF]
International Conference on Database Theory, 2019 Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the treewidth of a ...
Silviu Maniu, P. Senellart, Suraj Jog
semanticscholar +1 more source
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
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
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 Low Treewidth Approximations of Conjunctive Queries [PDF]
, 2012 We recently initiated the study of approximations of conjunctive queries within classes that admit tractable query evaluation (with respect to combined complexity).
Barcelo, Pablo +2 more
core +2 more sources
On the Satisfiability of Quantum Circuits of Small Treewidth
, 2016 It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results to the quantum
Oliveira, Mateus de Oliveira
core +1 more source