Size of the largest components in random planar maps

Zhicheng Gao, Nicholas C. Wormald

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)


Bender, Richmond, and Wormald showed that in almost all planar 3-connected triangulations (or dually, 3-connected cubic maps) with n edges, the largest 4-connected triangulation (or dually, the largest cyclically 4-edge-connected cubic components) has about n/2 edges. In this paper, we derive some general results about the size of the largest component and apply them to a variety of types of planar maps.

Original languageEnglish
Pages (from-to)217-228
Number of pages12
JournalSIAM Journal on Discrete Mathematics
Issue number2
Publication statusPublished - 1999
Externally publishedYes

Cite this