Synapse
⌘+K
Synapse
PulseExploreClubsResearchersJournals
Instagram
HomeClubsExplore
December 18, 2013Open Access

A bijection for plane graphs and its applications

View Full Paper
Ask AI
Bookmark
Share

Authors

OBOlivier BernardiGCGwendal ColletÉFÉric Fusy

Discussion

Loading...

Member takes

Overview

Combinatorial analysis reveals a bijection to oriented binary trees in rooted plane graphs, facilitating exact counting and efficient random sampling.

Key Points

  • Establish a structural bijection for plane graphs to resolve counting and random generation problems parameterized by vertices and edges.
  • Constructed an explicit bijective mapping between plane graphs with a triangular outer face and a defined family of oriented binary trees.
  • Tracked vertex and edge counts across the bijection and integrated Bóna's bijection to establish cross-domain combinatorial links.
  • Derived closed-form counting formulas for rooted plane graphs with arbitrary outer faces based on vertex and edge counts.
  • Developed an efficient algorithm for the exact random sampling of rooted plane graphs.
  • Established a direct bijective connection between rooted plane graphs and 1342-avoiding permutations.

Cite This Study

Bernardi et al. (2013) studied this question.

synapsesocial.com/papers/6a1e8cc459c40dbc7b560484https://doi.org/10.1137/1.9781611973204.5
View Full Paper
Ask AI
Bookmark
Share