Related papers: Computational Complexity of Covering Two-vertex Mu…
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a…
In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to…
Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems TEMPORAL VERTEX COVER (or TVC) and SLIDING-WINDOW TEMPORAL VERTEX COVER(or $\Delta$-TVC for time-windows of a fixed-length $\Delta$)…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
We consider the existence and construction of \textit{biclique covers} of graphs, consisting of coverings of their edge sets by complete bipartite graphs. The \textit{size} of such a cover is the sum of the sizes of the bicliques.…
Orbits of graphs under local complementation (LC) and edge local complementation (ELC) have been studied in several different contexts. For instance, there are connections between orbits of graphs and error-correcting codes. We define a new…
A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube $Q_d$ to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their…
A simple topological graph T = (V(T), E(T)) is a drawing of a graph in the plane where every two edges have at most one common point (an endpoint or a crossing) and no three edges pass through a single crossing. Topological graphs G and H…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
The neighborhood complex of a graph was introduced by Lov\'asz to provide topological lower bounds on chromatic number. More general homomorphism complexes of graphs were further studied by Babson and Kozlov. Such `Hom complexes' are also…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…