Characterizing 3-connected planar graphs and graphic matroids

: 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 Contract grant sponsor: CNPq; Contract grant numbers: 301178/05-4; 502048/07-7; 48567/07-7; Contract grant sponsor: FAPESP/CNPq; Contract grant number: 2003/09925-5. Journal of Graph Theory ᭧ 2009 Wiley Periodicals, Inc. 1 

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Manoel Lemos, Talmage James Reid, Haidong Wu
• Keywords: 3-connected Graphic Matroids, Contract Grant, Contract Grant Number, JGT 2010