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

Fingerprint

Intersection Graphs
Adjacency Matrix
End point
Graph in graph theory
Bipartite Graph
Horizontal
Vertical
Polynomials
Line
Linear Time
Slope
Polynomial time
If and only if
Partial
Drawing
Class

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Recognition and drawing of stick graphs. / De Luca, Felice; Hossain, Md Iqbal; Kobourov, Stephen G; Lubiw, Anna; Mondal, Debajyoti.

In: Theoretical Computer Science, 01.01.2019.

Research output: Contribution to journalArticle

De Luca, Felice ; Hossain, Md Iqbal ; Kobourov, Stephen G ; Lubiw, Anna ; Mondal, Debajyoti. / Recognition and drawing of stick graphs. In: Theoretical Computer Science. 2019.
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