TY - GEN

T1 - Touching triangle representations for 3-connected planar graphs

AU - Kobourov, Stephen G.

AU - Mondal, Debajyoti

AU - Nishat, Rahnuma Islam

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - A touching triangle graph (TTG) representation of a planar graph is a planar drawing Γ of the graph, where each vertex is represented as a triangle and each edge e is represented as a side contact of the triangles that correspond to the end vertices of e. We call Γ a proper TTG representation if Γ determines a tiling of a triangle, where each tile corresponds to a distinct vertex of the input graph. In this paper we prove that every 3-connected cubic planar graph admits a proper TTG representation. We also construct proper TTG representations for parabolic grid graphs and the graphs determined by rectangular grid drawings (e.g., square grid graphs). Finally, we describe a fixed-parameter tractable decision algorithm for testing whether a 3-connected planar graph admits a proper TTG representation.

AB - A touching triangle graph (TTG) representation of a planar graph is a planar drawing Γ of the graph, where each vertex is represented as a triangle and each edge e is represented as a side contact of the triangles that correspond to the end vertices of e. We call Γ a proper TTG representation if Γ determines a tiling of a triangle, where each tile corresponds to a distinct vertex of the input graph. In this paper we prove that every 3-connected cubic planar graph admits a proper TTG representation. We also construct proper TTG representations for parabolic grid graphs and the graphs determined by rectangular grid drawings (e.g., square grid graphs). Finally, we describe a fixed-parameter tractable decision algorithm for testing whether a 3-connected planar graph admits a proper TTG representation.

UR - http://www.scopus.com/inward/record.url?scp=84874129237&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874129237&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36763-2_18

DO - 10.1007/978-3-642-36763-2_18

M3 - Conference contribution

AN - SCOPUS:84874129237

SN - 9783642367625

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

SP - 199

EP - 210

BT - Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers

T2 - 20th International Symposium on Graph Drawing, GD 2012

Y2 - 19 September 2012 through 21 September 2012

ER -