Results 101 to 110 of about 13,679 (262)
Treewidth versus Clique Number. I. Graph Classes with a Forbidden Structure [PDF]
SIAM Journal on Discrete Mathematics, 2020 Treewidth is an important graph invariant, relevant for both structural and algorithmic reasons. A necessary condition for a graph class to have bounded treewidth is the absence of large cliques.
Clément Dallard +2 more
semanticscholar +1 more source
Constant-degree graph expansions that preserve the treewidth
, 2007 Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth.
I.L. Markov +13 more
core +2 more sources
Sparsest Cut on Bounded Treewidth Graphs: Algorithms and Hardness Results [PDF]
, 2013 We give a 2-approximation algorithm for Non-Uniform Sparsest Cut that runs in time $n^{O(k)}$, where $k$ is the treewidth of the graph. This improves on the previous $2^{2^k}$-approximation in time $\poly(n) 2^{O(k)}$ due to Chlamt\'a\v{c} et al.
Gupta, Anupam +2 more
core +2 more sources
Structural properties of graph products
Journal of Graph Theory, Volume 109, Issue 2, Page 107-136, June 2025.Abstract Dujmovć, Joret, Micek, Morin, Ueckerdt, and Wood established that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path. Motivated by this result, this paper systematically studies various structural properties of cartesian, direct and strong products.
Robert Hickingbotham, David R. Wood
wiley +1 more source
On the k-rainbow domination in graphs with bounded tree-width
Electronic Journal of Graph Theory and Applications, 2021 Given a positive integer k and a graph G = (V, E), a function f from V to the power set of Ik is called a k-rainbow function if for each vertex v ∈ V, f(v)=∅ implies ∪u ∈ N(v)f(u)=Ik where N(v) is the set of all neighbors of vertex v and Ik = {1, …, k ...
M. Alambardar Meybodi +3 more
doaj +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
On Constrained Minimum Weight Edge Covers With Applications to Emergency Planning
Networks, Volume 85, Issue 3, Page 261-271, April 2025.ABSTRACT In this paper we present a new covering problem, called Min Cost q$$ q $$‐Single Location Cover, where we are given a fixed positive integer q$$ q $$, a finite ground set J$$ J $$, an integral positive demand dj$$ {d}_j $$ for each element j∈J$$ j\in J $$, a collection 𝒥 of subsets of J$$ J $$, an integral positive cost cS$$ {c}_S $$ and an ...
Shai Dimant, Sven O. Krumke
wiley +1 more source
Treewidth, crushing, and hyperbolic volume [PDF]
, 2019 We prove that there exists a universal constant $c$ such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most $c$ times its volume.
Maria, Clément, Purcell, Jessica S.
core +3 more sources
The complexity of the perfect matching‐cut problem
Journal of Graph Theory, Volume 108, Issue 3, Page 432-462, March 2025.Abstract PERFECT MATCHING‐CUT is the problem of deciding whether a graph has a perfect matching that contains an edge‐cut. We show that this problem is NP‐complete for planar graphs with maximum degree four, for planar graphs with girth five, for bipartite five‐regular graphs, for graphs of diameter three, and for bipartite graphs of diameter four.
Valentin Bouquet, Christophe Picouleau
wiley +1 more source
Tree-width and large grid minors in planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Graphs and ...
Alexander Grigoriev
doaj +1 more source