Results 71 to 80 of about 13,814 (224)
Parameterized Compilation Lower Bounds for Restricted CNF-formulas
, 2016 We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width measures.
A Darwiche +12 more
core +1 more source
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
Tree decompositions and social graphs
, 2016 Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales.
Adcock, Aaron B. +2 more
core +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
An Efficient Algorithm for Computing Network Reliability in Small Treewidth
, 2019 We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges.
Goharshady, Amir Kafshdar +1 more
core +1 more source
Discrete Mathematics, 2006 AbstractA set of vertices S⊆V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G-S of the graph, obtained by making S a clique in the subgraph of G, induced by W∪S. We show that such safe separators are a very powerful tool for preprocessing
Hans L. Bodlaender, Arie M. C. A. Koster
openaire +5 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
On the treewidths of graphs of bounded degree. [PDF]
PLoS One, 2015 In this paper, we develop a new technique to study the treewidth of graphs with bounded degree. We show that the treewidth of a graph G = (V, E) with maximum vertex degree d is at most [Formula: see text] for sufficiently large d, where C is a constant.
Song Y, Yu M.
europepmc +6 more sources
Lower Bounds for the Complexity of Monadic Second-Order Logic
, 2010 Courcelle's famous theorem from 1990 states that any property of graphs definable in monadic second-order logic (MSO) can be decided in linear time on any class of graphs of bounded treewidth, or in other words, MSO is fixed-parameter tractable in linear
Kreutzer, Stephan, Tazari, Siamak
core +2 more sources