Partitions of complete geometric graphs into plane trees

Prosenjit Bose, Ferran Hurtado, Eduardo Rivera-Campo, David R. Wood

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

Consider the following question: does every complete geometric graph K 2n have a partition of its edge set into n plane spanning trees? We approach this problem from three directions. First, we study the case of convex geometric graphs. It is well known that the complete convex graph K 2n has a partition into n plane spanning trees. We characterise all such partitions. Second, we give a sufficient condition, which generalises the convex case, for a complete geometric graph to have a partition into plane spanning trees. Finally, we consider a relaxation of the problem in which the trees of the partition are not necessarily spanning. We prove that every complete geometric graph K n can be partitioned into at most n-√n/12 plane trees. This is the best known bound even for partitions into plane subgraphs.
Original languageEnglish
Pages (from-to)116-125
Number of pages10
JournalComputational Geometry: Theory and Applications
Volume34
Issue number2
DOIs
Publication statusPublished - 2006
Externally publishedYes

Cite this