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 publicationFundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings
Pages145-156
Number of pages12
DOIs
Publication statusPublished - 9 Nov 2009
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)0302-9743
ISSN (Electronic)1611-3349

Other

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

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ghosh, S. K., & Sinha, K. (2009). On convex greedy embedding conjecture for 3-connected planar graphs. In Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings (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