### Abstract

In the context of geographic routing, Papadimitriou and Ratajczak conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, greedy embedding conjecture has been resolved, though the construction do not result in a drawing that is planar and convex. In this work we consider the planar convex greedy embedding conjecture and make some progress. We show that in planar convex greedy embedding of a graph, weight of the maximum weight spanning tree (T) and weight of the minimum weight spanning tree (MST) satisfies , (|V

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 145-156 |

Number of pages | 12 |

Volume | 5699 LNCS |

DOIs | |

Publication status | Published - 9 Nov 2009 |

Externally published | Yes |

Event | 17th International Symposium on Fundamentals of Computation Theory, FCT 2009 - Wroclaw, Poland Duration: 2 Sep 2009 → 4 Sep 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5699 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 17th International Symposium on Fundamentals of Computation Theory, FCT 2009 |
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Country | Poland |

City | Wroclaw |

Period | 2/9/09 → 4/9/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5699 LNCS, pp. 145-156). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5699 LNCS). https://doi.org/10.1007/978-3-642-03409-1_14

**On convex greedy embedding conjecture for 3-connected planar graphs.** / Ghosh, Subhas Kumar; Sinha, Koushik.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5699 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5699 LNCS, pp. 145-156, 17th International Symposium on Fundamentals of Computation Theory, FCT 2009, Wroclaw, Poland, 2/9/09. https://doi.org/10.1007/978-3-642-03409-1_14

}

TY - GEN

T1 - On convex greedy embedding conjecture for 3-connected planar graphs

AU - Ghosh, Subhas Kumar

AU - Sinha, Koushik

PY - 2009/11/9

Y1 - 2009/11/9

N2 - In the context of geographic routing, Papadimitriou and Ratajczak conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, greedy embedding conjecture has been resolved, though the construction do not result in a drawing that is planar and convex. In this work we consider the planar convex greedy embedding conjecture and make some progress. We show that in planar convex greedy embedding of a graph, weight of the maximum weight spanning tree (T) and weight of the minimum weight spanning tree (MST) satisfies , (|V

AB - In the context of geographic routing, Papadimitriou and Ratajczak conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, greedy embedding conjecture has been resolved, though the construction do not result in a drawing that is planar and convex. In this work we consider the planar convex greedy embedding conjecture and make some progress. We show that in planar convex greedy embedding of a graph, weight of the maximum weight spanning tree (T) and weight of the minimum weight spanning tree (MST) satisfies , (|V

UR - http://www.scopus.com/inward/record.url?scp=70350635758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350635758&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03409-1_14

DO - 10.1007/978-3-642-03409-1_14

M3 - Conference contribution

SN - 364203408X

SN - 9783642034084

VL - 5699 LNCS

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

SP - 145

EP - 156

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

ER -