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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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Clones in Matroids
by
Talmage James Reid
The University of Mississippi
Coauthors: Jakayla Robbins, Haidong Wu, Xiangqian Zhou

Two elements of a matroid are clones if the map that interchanges the elements and fixes all other elements is an isomorphism. Whittle conjectured that if M is a 3-connected quarternary matroid with a clone pair {e, f}, then M \e, f and M/ e, f are both binary. We answer Whittle's conjecture affirmatively.

Date received: April 20, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-27.