Graph theory is a fundamental branch of mathematics that studies networks consisting of
nodes (vertices) and their connections (edges). Extensive research has been conducted on …

A string graph is an intersection graph of curves in the plane. A k-string graph is a graph with
a string representation in which every pair of curves intersects in at most k points. We …

We consider Independent Set and Dominating Set restricted to VPG graphs (or, equivalently,
string graphs). We show that they both remain $\mathsf {NP} $-hard on $ B_0 $-VPG graphs …

A graph G is an edge intersection graph of paths on a grid (or EPG graph) if its vertices can
be represented as simple paths on a rectangular grid, such that two vertices are adjacent in …

In this paper, we explore geometric discriminating code and set cover problems with k-bend
paths. We first demonstrate that both the discriminating code problem and the set cover …

Abstract A contact B 0–VPG graph is a graph for which there exists a collection of nontrivial
pairwise interiorly disjoint horizontal and vertical segments in one-to-one correspondence …