### 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.

Original language | English (US) |
---|---|

Title of host publication | Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers |

Pages | 199-210 |

Number of pages | 12 |

DOIs | |

State | Published - Feb 26 2013 |

Event | 20th International Symposium on Graph Drawing, GD 2012 - Redmond, WA, United States Duration: Sep 19 2012 → Sep 21 2012 |

### Publication series

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

Volume | 7704 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 20th International Symposium on Graph Drawing, GD 2012 |
---|---|

Country | United States |

City | Redmond, WA |

Period | 9/19/12 → 9/21/12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Touching triangle representations for 3-connected planar graphs'. Together they form a unique fingerprint.

## Cite this

*Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers*(pp. 199-210). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7704 LNCS). https://doi.org/10.1007/978-3-642-36763-2_18