Edge intersection graphs of single bend paths on a grid

Martin Charles Golumbic, Marina Lipshteyn, Michal Stern

Research output: Contribution to journalArticlepeer-review


We combine the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model to introduce the edge intersection graphs of paths on a grid. Let P be a collection of nontrivial simple paths on a grid G. We define the edge intersection graph EPG(P) of P to have vertices which correspond to the members of P, such that two vertices are adjacent in EPG(P) if the corresponding paths in P share an edge in G.An undirected graph G is called an edge intersection graph of paths on a grid (EPG) if G = EPG(P) for some P and G, and (P, G) is an EPG representation of G. We prove that every graph is an EPG graph. A turn of a path at a grid point is called a bend. We consider here EPG representations in which every path has at most a single bend, called B 1-EPG representations and the corresponding graphs are called B 1-EPG graphs. We prove that any tree is a B1-EPG graph. Moreover, we give a structural property that enables one to generate non B 1-EPG graphs. Furthermore, we characterize the representation of cliques and chordless 4-cycles in B1-EPG graphs. We also prove that single bend paths on a grid have Strong Helly number 3.

Original languageEnglish
Pages (from-to)130-138
Number of pages9
Issue number3
StatePublished - Oct 2009


  • Intersection graphs
  • Path bend
  • Paths on a grid

ASJC Scopus subject areas

  • Information Systems
  • Computer Networks and Communications


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