Related papers: The parameterised complexity of computing the maxi…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
A map graph is a graph admitting a representation in which vertices are nations on a spherical map and edges are shared curve segments or points between nations. We present an explicit fixed-parameter tractable algorithm for recognizing map…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of…
Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…
Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property…
In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in…
The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it…
Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. Recently a new characterization of…
In this paper, we consider the problem of maximizing the spread of influence through a social network. Given a graph with a threshold value~$thr(v)$ attached to each vertex~$v$, the spread of influence is modeled as follows: A vertex~$v$…
The Target Set Selection problem takes as an input a graph $G$ and a non-negative integer threshold $ \mbox{thr}(v) $ for every vertex $v$. A vertex $v$ can get active as soon as at least $ \mbox{thr}(v) $ of its neighbors have been…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
We give alternative definitions for maximum matching width, e.g. a graph $G$ has $\operatorname{mmw}(G) \leq k$ if and only if it is a subgraph of a chordal graph $H$ and for every maximal clique $X$ of $H$ there exists $A,B,C \subseteq X$…