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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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EULERIAN AND BIPARTITE ORIENTABLE MATROIDS

EULERIAN AND BIPARTITE ORIENTABLE MATROIDS

Chapter:
(p.11) 2 EULERIAN AND BIPARTITE ORIENTABLE MATROIDS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Laura E. Chávez Lomelí

Luis A. Goddyn

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0002

This chapter focuses on extending the characterizations of Eulerian graphs via orientations. An Eulerian tour of a graph G induces an orientation with the property that every cocircuit (minimal edge cut) in G is traversed an equal number of times in each direction. In this sense, the orientation can be considered balanced. Applying duality to planar graphs, these notions produce characterizations of bipartite graphs. These notions are further extended to oriented matroids.

Keywords:   Eulerian graphs, orientations, oriented matroids, bipartite graphs

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