TY - GEN

T1 - Straight-line grid drawings of 3-connected 1-planar graphs

AU - Alam, Md Jawaherul

AU - Brandenburg, Franz J.

AU - Kobourov, Stephen G.

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

AB - A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

UR - http://www.scopus.com/inward/record.url?scp=84891887533&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-03841-4_8

DO - 10.1007/978-3-319-03841-4_8

M3 - Conference contribution

AN - SCOPUS:84891887533

SN - 9783319038407

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

SP - 83

EP - 94

BT - Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers

PB - Springer-Verlag

T2 - 21st International Symposium on Graph Drawing, GD 2013

Y2 - 23 September 2013 through 25 September 2013

ER -