Related papers: On the bend number of circular-arc graphs as edge …

In this paper we continue the study of the edge intersection graphs of one (or zero) bend paths on a rectangular grid. That is, the edge intersection graphs where each vertex is represented by one of the following shapes:…

We introduce a new class of intersection graphs, the edge intersection graphs of paths on a triangular grid, called EPGt graphs. We show similarities and differences from this new class to the well-known class of EPG graphs. A turn of a…

If a graph $G$ can be represented by means of paths on a grid, such that each vertex of $G$ corresponds to one path on the grid and two vertices of $G$ are adjacent if and only if the corresponding paths share a grid edge, then this graph…

Golumbic, Lipshteyn, and Stern defined in 2009 the class of EPG graphs, the intersection graph class of edge paths on a grid. An EPG graph $G$ is a graph that admits a representation where its vertices correspond to paths in a grid $Q$,…

We show that every 4-connected planar graph has a $B_3$-EPG representation, i.e., every vertex is represented by a curve on the grid with at most three bends, and two vertices are adjacent if and only if the corresponding curves share an…

In this paper we present a characterisation, by an infinite family of minimal forbidden induced subgraphs, of proper circular arc graphs which are intersection graphs of paths on a grid, where each path has at most one bend (turn).

In this paper we continue the systematic study of Contact graphs of Paths on a Grid (CPG graphs) initiated in [Deniz et al., 2018]. A CPG graph is a graph for which there exists a collection of pairwise interiorly disjoint paths on a grid…

An EPG-representation of a graph $G$ is a collection of paths in a plane square grid, each corresponding to a single vertex of $G$, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In…

In this paper, we are interested in the edge intersection graphs of paths of a grid where each path has at most one bend, called B1-EPG graphs and first introduced by Golumbic et al (2009). We also consider a proper subclass of B1-EPG, the…

In a representation of a graph $G$ as an edge intersection graph of paths on a grid (EPG) every vertex of $G$ is represented by a path on a grid and two paths share a grid edge iff the corresponding vertices are adjacent. In a monotonic EPG…

We investigate edge-intersection graphs of paths in the plane grid, regarding a parameter called the bend-number. I.e., every vertex is represented by a grid path and two vertices are adjacent if and only if the two grid paths share at…

Given a tree and a set ${\cal P}$ of non-trivial simple paths on it, $VPT({\cal P})$ is the VPT graph (i.e. the vertex intersection graph) of the paths ${\cal P}$ of the tree $T$, and $EPT({\cal P})$ is the EPT graph (i.e. the edge…

The families EPT (resp. EPG) Edge Intersection Graphs of Paths in a tree (resp. in a grid) are well studied graph classes. Recently we introduced the graph classes Edge-Intersecting and Non-Splitting Paths in a Tree ENPT, and in a Grid…

A piecewise linear curve in the plane made up of $k+1$ line segments, each of which is either horizontal or vertical, with consecutive segments being of different orientation is called a $k$-bend path. Given a graph $G$, a collection of…

In this paper we study properties of intersection graphs of k-bend paths in the rectangular grid. A k-bend path is a path with at most k 90 degree turns. The class of graphs representable by intersections of k-bend paths is denoted by…

EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class $B_k$-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most $k$ bends.…

We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called $B_0$-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time…

A $k$-bend path is a non-self-intersecting polyline in the plane made of at most $k+1$ axis-parallel line segments. B$_k$-VPG is the class of graphs which can be represented as intersection graphs of $k$-bend paths in the same plane. In…

In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are…

Given a tree and a set P of non-trivial simple paths on it, VPT(P) is the VPT graph (i.e. the vertex intersection graph) of the paths P, and EPT(P) is the EPT graph (i.e. the edge intersection graph) of P. These graphs have been extensively…