Recognition and drawing of stick graphs

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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, we present an O(|A|3|B|3 -time algorithm. When neither ordering is given, we present some partial results about graphs that are, or are not, Stick representable.

Original languageEnglish (US)
Title of host publicationGraph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings
EditorsTherese Biedl, Andreas Kerren
PublisherSpringer-Verlag
Pages303-316
Number of pages14
ISBN (Print)9783030044138
DOIs
StatePublished - Jan 1 2018
Event26th International Symposium on Graph Drawing and Network Visualization, GD 2018 - Barcelona, Spain
Duration: Sep 26 2018Sep 28 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11282 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th International Symposium on Graph Drawing and Network Visualization, GD 2018
CountrySpain
CityBarcelona
Period9/26/189/28/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    De Luca, F., Hossain, M. I., Kobourov, S. G., Lubiw, A., & Mondal, D. (2018). Recognition and drawing of stick graphs. In T. Biedl, & A. Kerren (Eds.), Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings (pp. 303-316). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11282 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-04414-5_21