Document Type
Article
Publication Date
11-1-2011
Abstract
In a 1965 paper, Erdos remarked that a graph G has a bipartite subgraph that has at least half as many edges as G. The purpose of this note is to prove a matroid analogue of Erdos's original observation. It follows from this matroid result that every loopless binary matroid has a restriction that uses more than half of its elements and has no odd circuits; and, for 2≤k≤5, every bridgeless graph G has a subgraph that has a nowhere-zero k-flow and has more than k-1/k|E(G)| edges. © 2011 Elsevier Ltd.
Publication Source (Journal or Book title)
European Journal of Combinatorics
First Page
1199
Last Page
1202
Recommended Citation
Oxley, J. (2011). On bipartite restrictions of binary matroids. European Journal of Combinatorics, 32 (8), 1199-1202. https://doi.org/10.1016/j.ejc.2011.04.005
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