TY - GEN

T1 - Recognition and drawing of stick graphs

AU - De Luca, Felice

AU - Hossain, Md Iqbal

AU - Kobourov, Stephen

AU - Lubiw, Anna

AU - Mondal, Debajyoti

N1 - Funding Information:
Acknowledgments. The research of A. Lubiw and D. Mondal is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). Also, this work is supported in part by NSF grants CCF-1423411 and CCF-1712119.
Publisher Copyright:
© Springer Nature Switzerland AG 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-04414-5_21

DO - 10.1007/978-3-030-04414-5_21

M3 - Conference contribution

AN - SCOPUS:85059088195

SN - 9783030044138

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 303

EP - 316

BT - Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings

A2 - Biedl, Therese

A2 - Kerren, Andreas

PB - Springer-Verlag

T2 - 26th International Symposium on Graph Drawing and Network Visualization, GD 2018

Y2 - 26 September 2018 through 28 September 2018

ER -