Touching triangle representations for 3-connected planar graphs

Authors:
Stephen G. Kobourov;Debajyoti Mondal;Rahnuma Islam Nishat
Affiliations:
Department of Computer Science, University of Arizona;Department of Computer Science, University of Manitoba, Canada;Department of Computer Science, University of Victoria, Canada
Venue:
GD'12 Proceedings of the 20th international conference on Graph Drawing
Year:
2012

Citing 9
Cited 0

Interval representations of planar graphs

Journal of Combinatorial Theory Series B
On Floor-Plan of Plane Graphs

SIAM Journal on Computing
Exact algorithms for NP-hard problems: a survey

Combinatorial optimization - Eureka, you shrink!
Rectangular drawings of planar graphs

Journal of Algorithms
Compact floor-planning via orderly spanning trees

Journal of Algorithms
Barycentric systems and stretchability

Discrete Applied Mathematics
Rectangular layouts and contact graphs

ACM Transactions on Algorithms (TALG)
On touching triangle graphs

GD'10 Proceedings of the 18th international conference on Graph drawing
Optimal Polygonal Representation of Planar Graphs

Algorithmica - Special Issue: Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.