Related papers: Diverse Collections in Matroids and Graphs
In this paper, we address the weighted linear matroid intersection problem from the computation of the degree of the determinants of a symbolic matrix. We show that a generic algorithm computing the degree of noncommutative determinants,…
We generalize the polynomial-time solvability of $k$-\textsc{Diverse Minimum s-t Cuts} (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three…
The problem of combinatorially determining the rank of the 3-dimensional bar-joint {\em rigidity matroid} of a graph is an important open problem in combinatorial rigidity theory. Maxwell's condition states that the edges of a graph $G=(V,…
We study the problem Symmetric Directed Multicut from a parameterized complexity perspective. In this problem, the input is a digraph $D$, a set of cut requests $C=\{(s_1,t_1),\ldots,(s_\ell,t_\ell)\}$ and an integer $k$, and the task is to…
In the Exact Matching Problem (EM), we are given a graph equipped with a fixed coloring of its edges with two colors (red and blue), as well as a positive integer $k$. The task is then to decide whether the given graph contains a perfect…
We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of X-HitPack asks: Can removing k (deletable) vertices of a graph G…
A minimum dominating set in a graph is a minimum set of vertices such that every vertex of the graph either belongs to it, or is adjacent to one vertex of this set. This mathematical object is of high relevance in a number of applications…
A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists…
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…
A 2-packing set for an undirected, weighted graph G=(V,E,w) is a subset S of the vertices V such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2-Packing Set problem that asks for a 2-packing set of…
We give a combinatorial condition for the existence of efficient, LP-based FPT algorithms for a broad class of graph-theoretical optimisation problems. Our condition is based on the notion of biased graphs known from matroid theory.…
Consider a planar graph $G=(V,E)$ with polynomially bounded edge weight function $w:E\to [0, poly(n)]$. The main results of this paper are NC algorithms for the following problems: - minimum weight perfect matching in $G$, - maximum…
We present a framework for the complexity classification of parameterized counting problems that can be formulated as the summation over the numbers of homomorphisms from small pattern graphs H_1,...,H_l to a big host graph G with the…
We study the complexity of counting (weighted) planar graph homomorphism problem $\tt{Pl\text{-}GH}(M)$ parametrized by an arbitrary symmetric non-negative real valued matrix $M$. For matrices with pairwise distinct diagonal values, we…
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
In this paper, we introduce a connection between two classical concepts of graph theory: \; metric dimension and distinguishing number. For a given graph $G$, let ${\rm dim}(G)$ and $D(G)$ represent its metric dimension and distinguishing…
A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…
We study the parallel (adaptive) complexity of the classic problem of finding a basis in an $n$-element matroid, given access via an \emph{independence oracle}. In this model, the algorithm may submit polynomially many independence queries…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
In 30's Hassler Whitney considered and completely solved the problem $(WP)$ of describing the classes of graphs $G$ having the same cycle matroid $M(G)$. A natural analog $(WP)'$ of Whitney's problem $(WP)$ is to describe the classes of…