Recognition and drawing of stick graphs

Felice De Luca, Md Iqbal Hossain, Stephen G Kobourov, Anna Lubiw, Debajyoti Mondal

Research output: Contribution to journalArticle

Abstract

A Stick graph is an intersection graph of axis-aligned segments such that the left end-points of the horizontal segments and the bottom end-points of the vertical segments lie on a “ground line,” a line with slope −1. It is an open question to decide in polynomial time whether a given bipartite graph G with bipartition A∪B has a Stick representation where the vertices in A and B correspond to horizontal and vertical segments, respectively. We prove that G has a Stick representation if and only if there are orderings of A and B such that G's bipartite adjacency matrix with rows A and columns B excludes three small ‘forbidden’ submatrices. This is similar to characterizations for other classes of bipartite intersection graphs. We present an algorithm to test whether given orderings of A and B permit a Stick representation respecting those orderings, and to find such a representation if it exists. The algorithm runs in time linear in the size of the adjacency matrix. For the case when only the ordering of A is given, or neither ordering is given, we present some partial results about graphs that are, or are not, Stick representable.

Original languageEnglish (US)
JournalTheoretical Computer Science
DOIs
StateAccepted/In press - Jan 1 2019

Keywords

  • Bipartite Graphs
  • Graph Drawing
  • Intersection Graphs
  • Stick Graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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