Related papers: Revising Johnson's table for the 21st century
A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially…
The concept of $k$-planarity is extensively studied in the context of Beyond Planarity. A graph is $k$-planar if it admits a drawing in the plane in which each edge is crossed at most $k$ times. The local crossing number of a graph is the…
Structural graph parameters play an important role in parameterized complexity, including in kernelization. Notably, vertex cover, neighborhood diversity, twin-cover, and modular-width have been studied extensively in the last few years.…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently…
Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
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…
The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some…
The problem of efficiently characterizing degree sequences of simple hypergraphs is a fundamental long-standing open problem in Graph Theory. Several results are known for restricted versions of this problem. This paper adds to the list of…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
Let $G$ be a graph on $n$ vertices and $\mathrm{STAB}_k(G)$ be the convex hull of characteristic vectors of its independent sets of size at most $k$. We study extension complexity of $\mathrm{STAB}_k(G)$ with respect to a fixed parameter…
We systematically explore a class of constrained optimization problems with linear objective function and constraints that are linear combinations of logarithms of the optimization variables. Such problems can be viewed as a generalization…
We consider the problem of finding a Hamiltonian path or a Hamiltonian cycle with precedence constraints in the form of a partial order on the vertex set. We show that the path problem is $\mathsf{NP}$-complete for graphs of pathwidth 4…
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…
We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This…
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…
Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such…