# Edge intersection graphs of paths on a grid

Martin Charles Golumbic, Gila Morgenstern

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

## Abstract

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 the graph, if and only if their corresponding paths share at least one edge of the grid. EPG graphs were first introduced and studied by M. C. Golumbic, M. Lipshteyn, and M. Stern. In that paper, the authors show that every graph is an EPG graph. Moreover, it always has a monotonic EPG representation, namely, one where each path is ascending in rows and columns. A turn of a path at a grid-point is called a bend, and a graph is called a k-bend EPG graph (denoted Bk-EPG), if it has an EPG representation in which each path has at most k bends. A graph G is chordal if G does not contain a chordless cycle of size at least four, often called a hole.

Original language English 50 years of Combinatorics, Graph Theory, and Computing CRC Press 193-209 17 9781000751833 9780367235031 Published - 15 Nov 2019