Related papers: A CSP approach to Graph Sandwich Problems
We introduce the Multicolored Graph Realization problem (MGRP). The input to the problem is a colored graph $(G,\varphi)$, i.e., a graph together with a coloring on its vertices. We can associate to each colored graph a cluster graph…
The problem of packing as many subgraphs isomorphic to $H \in \mathcal H$ as possible in a graph for a class $\mathcal H$ of graphs is well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be…
Let \Gamma be a structure with a finite relational signature and a first-order definition in (R;*,+) with parameters from R, that is, a relational structure over the real numbers where all relations are semi-algebraic sets. In this article,…
Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are…
In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must…
We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…
What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on…
It was recently shown \cite{STV} that satisfiability is polynomially solvable when the incidence graph is an interval bipartite graph (an interval graph turned into a bipartite graph by omitting all edges within each partite set). Here we…
In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…
We study the complexity of the parameterised counting constraint satisfaction problem: given a set of constraints over a set of variables and a positive integer $k$, how many ways are there to assign $k$ variables to 1 (and the others to 0)…
A constraint satisfaction problem (CSP), $\textsf{Max-CSP}(\mathcal{F})$, is specified by a finite set of constraints $\mathcal{F} \subseteq \{[q]^k \to \{0,1\}\}$ for positive integers $q$ and $k$. An instance of the problem on $n$…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
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.…
A path in an(a) edge(vertex)-colored graph is called \emph{a conflict-free path} if there exists a color used on only one of its edges(vertices). An(A) edge(vertex)-colored graph is called \emph{conflict-free (vertex-)connected} if there is…
We introduce the framework of the left-hand side restricted promise constraint satisfaction problem, which includes problems like approximating clique number of a graph. We study the parameterized complexity of problems in this class and…
It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a…
A clique of a graph is a maximal set of vertices of size at least 2 that induces a complete graph. A $k$-clique-colouring of a graph is a colouring of the vertices with at most $k$ colours such that no clique is monochromatic. D\'efossez…
Let $G$ be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. Suppose that we are given two list edge-colorings $f_0$ and $f_r$ of $G$, and asked…
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 study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop…