Name
Abstract | ||
|---|---|---|
This article presents new bijections on planar maps. At first a bijection is established between bipolar orientations on planar maps and specific ''transversal structures'' on triangulations of the 4-gon with no separating 3-cycle, which are called irreducible triangulations. This bijection specializes to a bijection between rooted non-separable maps and rooted irreducible triangulations. This yields in turn a bijection between rooted loopless maps and rooted triangulations, based on the observation that loopless maps and triangulations are decomposed in a similar way into components that are respectively non-separable maps and irreducible triangulations. This gives another bijective proof (after Wormald's construction published in 1980) of the fact that rooted loopless maps with n edges are equinumerous to rooted triangulations with n inner vertices. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.ejc.2009.02.008 | Eur. J. Comb. |
Keywords | Field | DocType |
bijections | Discrete mathematics,Combinatorics,Bijection,Vertex (geometry),Bijection, injection and surjection,Transversal (geometry),Bijective proof,Planar,Mathematics | Journal |
Volume | Issue | ISSN |
31 | 1 | 0195-6698 |
Citations | PageRank | References |
1 | 0.37 | 13 |
Authors | ||
1 | ||