Graph theory is afundamental branch of mathematicsthat studiesnetworksconsisting of
nodes (vertices) and their connections (edges). Extensive research has been conducted on …

Interval graphs represent vertices as intervals on the real line, with edges denoting
overlapping intervals, while proper interval graphs prevent one interval from being fully …

The⌞-intersection graphs are the graphs that have a representation as intersection graphs
of axis-parallel⌞ shapes in the plane. A subfamily of these graphs are {⌞,|,–}-contact graphs …

A graph G is a max point-tolerance (MPT) graph if each vertex v of G can be mapped to a
pointed-interval (I v, pv) where I v is an interval of R and pv∈ I v such that uv is an edge of G …

An L-shape is the union of a horizontal and a vertical segment with a common endpoint.
These come in four rotations:,, and. A k-bend path is a simple path in the plane, whose …

We present two approximation algorithms for the maximum independent set (MIS) problem
over the class of B_1 B 1-VPG graphs and also for the subclass, equilateral B_1 B 1-VPG …

A piecewise linear simple 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 …

We study contact representations of non-planar graphs in which vertices are represented by
axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries …

A square-contact representation of a planar graph $ G=(V, E) $ maps vertices in $ V $ to
interior-disjoint axis-aligned squares in the plane and edges in $ E $ to adjacencies …

A morph is a continuous transformation between two representations of a graph. We
consider the problem of morphing between contact representations of a plane graph. In an F …