Related papers: Schaefer's theorem for graphs
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
We introduce an NP-complete graph decision problem, the "Multi-stage graph Simple Path" (abbr. MSP) problem, which focuses on determining the existence of specific "global paths" in a graph $G$. We show that the MSP problem can be solved in…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
The independence number of a tree decomposition is the size of a largest independent set contained in a single bag. The tree-independence number of a graph $G$ is the minimum independence number of a tree decomposition of $G$. As shown…
We prove a complexity dichotomy theorem for symmetric complex-weighted Boolean #CSP when the constraint graph of the input must be planar. The problems that are #P-hard over general graphs but tractable over planar graphs are precisely…
We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- presents itself as the strength of the corresponding De…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in the other part.…
What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 "Graph Restrictions and Their Effect" of D. S. Johnson's Ongoing guide, where several puzzles were proposed…
It is shown that graph-theoretic problem CLIQUE can't be solved in polynomial time by any deterministic TM. This upgrades the well-known partial result that claims only monotone unsolvability thereof, and eventually implies P $\neq$ NP as…
In the Boolean maximum constraint satisfaction problem - Max CSP$(\Gamma)$ - one is given a collection of weighted applications of constraints from a finite constraint language $\Gamma$, over a common set of variables, and the goal is to…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Constraint satisfaction (CSP) and structure isomorphism (SI) are among the most well-studied computational problems in Computer Science. While neither problem is thought to be in $\texttt{PTIME},$ much work is done on $\texttt{PTIME}$…
One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…
We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…
We study consistent query answering via different graph representations. First, we introduce solution-conflict hypergraphs in which nodes represent facts and edges represent either conflicts or query solutions. Considering a monotonic query…
Many tractable algorithms for solving the Constraint Satisfaction Problem (CSP) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance…
We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be formulated as that of completing…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…