Related papers: Compact Representation of Semilinear and Terrain-l…
There is a class of graphs with well-covered dimension equal to the simplicial clique number that contains all chordal graphs and infinitely many other graphs. These graphs generalize a result by Brown and Nowakowski on the well-covered…
A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are…
Let $C_{s,t}$ be the complete bipartite geometric graph, with $s$ and $t$ vertices on two distinct parallel lines respectively, and all $s t$ straight-line edges drawn between them. In this paper, we show that every complete bipartite…
Clustering trajectories is a central challenge when faced with large amounts of movement data such as GPS data. We study a clustering problem that can be stated as a geometric set cover problem: Given a polygonal curve of complexity $n$,…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
The biclique covering number of a bipartite graph G is the minimum number of complete bipartite subgraphs (bicliques) whose union contains every edge of G. In this little note we compare three lower bounds on the biclique covering number: A…
In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also…
We introduce a representation via (n+1)-colored graphs of compact n-manifolds with (possibly empty) boundary, which appears to be very convenient for computer aided study and tabulation. Our construction is ageneralization to arbitrary…
A universal representation theorem is derived that shows any graph is the intersection graph of one chordal graph, a number of co-bipartite graphs, and one unit interval graph. Central to the the result is the notion of the clique cover…
We show that any $3$-connected cubic plane graph on $n$ vertices, with all faces of size at most $6$, can be made bipartite by deleting no more than $\sqrt{(p+3t)n/5}$ edges, where $p$ and $t$ are the numbers of pentagonal and triangular…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
Recently, Daligault, Rao and Thomass\'e asked in [3] if every hereditary class which is well-quasi-ordered by the induced subgraph relation is of bounded clique-width. There are two reasons why this questions is interesting. First, it…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…
Detecting dense subgraphs from large graphs is a core component in many applications, ranging from social networks mining, bioinformatics. In this paper, we focus on mining dense subgraphs in a bipartite graph. The work is motivated by the…
In an EPG-representation of a graph $G$ each vertex is represented by a path in the rectangular grid, and $(v,w)$ is an edge in $G$ if and only if the paths representing $v$ an $w$ share a grid-edge. Requiring paths representing edges to be…
The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle…
We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number $\mathrm{Cov}(G)$ and the minimal rectifier network size $\mathrm{Rect}(G)$ of a bipartite graph $G$. We show that there exist graphs with…
An abstract $n$-polytope $\mathcal{P}$ is a partially-ordered set which captures important properties of a geometric polytope, for any dimension $n$. For even $n \ge 2$, the incidences between elements in the middle two layers of the Hasse…
The biclique cover number $(\text{bc})$ of a graph $G$ denotes the minimum number of complete bipartite (biclique) subgraphs to cover all the edges of the graph. In this paper, we show that $\text{bc}(G) \geq \lceil \log_2(\text{mc}(G^c))…