Related papers: Splitting Vertices in 2-Layer Graph Drawings
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural…
We consider a set of cliques in any multipartite graph with two vertices in each part. Moreover, we construct a class of peculiar polytopes. Key words: multipartite graph, clique, polytope.
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…
Bipartite graphs, formed by two vertex layers, arise as a natural fit for modeling the relationships between two groups of entities. In bipartite graphs, common neighborhood computation between two vertices on the same vertex layer is a…
Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…
The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper 10.1016/j.ejor.2014.05.042, the…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is \NP-hard. One way to allow for fewer crossings in practice are…
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…
Each finite and connected bipartite graph induces a finite collection of non-isomorphic dessins d'enfants, that is, $2$-cell embeddings of it into some closed orientable surface. We describe an algorithm to compute all these dessins…
Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly not much has been investigated for directed graphs. In this paper we study…
We consider hypergraph visualizations that represent vertices as points in the plane and hyperedges as curves passing through the points of their incident vertices. Specifically, we consider several different variants of this problem by (a)…
Graph partitioning is an important preprocessing step to distributed graph processing. In edge partitioning, the edge set of a given graph is split into $k$ equally-sized partitions, such that the replication of vertices across partitions…