On the circuit-spectrum of binary matroids

Authors:
Manoel Lemos;Talmage James Reid;Haidong Wu
Affiliations:
Departamento de Matematica, Universidade Federal de Pernambuco, Recife, Pernambuco 50740-540, Brazil;Department of Mathematics, The University of Mississippi, University, MS 38677, United States;Department of Mathematics, The University of Mississippi, University, MS 38677, United States
Venue:
European Journal of Combinatorics
Year:
2011

Citing 2
Cited 0

Matroids Having Small Circumference

Combinatorics, Probability and Computing
The 3-connected binary matroids with circumference 6 or 7

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Murty, in 1971, characterized the connected binary matroids with all circuits having the same size. We characterize the connected binary matroids with circuits of two different sizes, where the largest size is odd. As a consequence of this result we obtain both Murty's result and other results on binary matroids with circuits of only two sizes. We also show that it will be difficult to complete the general case of this problem.