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Matroid Duality from Topological Duality in Surfaces of Nonnegative Euler Characteristic

Published online by Cambridge University Press:  09 October 2002

DANIEL C. SLILATY
DANIEL C. SLILATY
Affiliation:
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA (e-mail: dslilaty@math.wright.edu)
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Abstract

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Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 5 , September 2002 , pp. 515 - 528
Copyright
2002 Cambridge University Press