Name
Abstract | ||
|---|---|---|
A well-known result of Tutte states that a 3-connected graph G is planar if and only if every edge of G is contained in exactly two induced non-separating circuits. Bixby and Cunningham generalized Tutte's result to binary matroids. We generalize both of these results and give new characterizations of both 3-connected planar graphs and 3-connected graphic matroids. Our main result determines when a natural necessary condition for a binary matroid to be graphic is also sufficient. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 165–174, 2010 |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1002/jgt.v64:2 | Journal of Graph Theory |
Keywords | Field | DocType |
connected graph,planar graph | Tutte 12-cage,Matroid,Topology,Discrete mathematics,Combinatorics,Tutte polynomial,Clique-sum,Polyhedral graph,Nowhere-zero flow,Graphic matroid,Mathematics,Branch-decomposition | Journal |
Volume | Issue | ISSN |
64 | 2 | 0364-9024 |
Citations | PageRank | References |
2 | 0.43 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Manoel Lemos | 1 | 83 | 19.44 |
| Talmage James Reid | 2 | 48 | 12.18 |
| Haidong Wu | 3 | 26 | 8.43 |