On convex greedy embedding conjecture for 3-connected planar graphs

Subhas Kumar Ghosh, Koushik Sinha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

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 languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages145-156
Number of pages12
Volume5699 LNCS
DOIs
Publication statusPublished - 9 Nov 2009
Externally publishedYes
Event17th International Symposium on Fundamentals of Computation Theory, FCT 2009 - Wroclaw, Poland
Duration: 2 Sep 20094 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5699 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other17th International Symposium on Fundamentals of Computation Theory, FCT 2009
CountryPoland
CityWroclaw
Period2/9/094/9/09

Fingerprint

Planar graph
Connected graph
Spanning tree
Euclidean plane
Routing
Graph in graph theory

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ghosh, S. K., & Sinha, K. (2009). On convex greedy embedding conjecture for 3-connected planar graphs. In 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5699 LNCS 2009. p. 145-156 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5699 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ghosh, SK & Sinha, K 2009, On convex greedy embedding conjecture for 3-connected planar graphs. in 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
Ghosh SK, Sinha K. On convex greedy embedding conjecture for 3-connected planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5699 LNCS. 2009. p. 145-156. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-03409-1_14
Ghosh, Subhas Kumar ; Sinha, Koushik. / On convex greedy embedding conjecture for 3-connected planar graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5699 LNCS 2009. pp. 145-156 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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