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Cocircuit coverings and packings for binary matroids

Published online by Cambridge University Press:  24 October 2008

James G. Oxley
James G. Oxley
Affiliation:
Mathematical Institute, Oxford
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Extract

If M is an arbitrary loopless matroid with ground set E(M) and rank function ρ, then let α(M) be the minimum size of a set of cocircuits of M, whose union is E(M), and let β(M) be the maximum size of a set of pairwise disjoint cocircuits of M. The following conjecture is based on Gallai's theorem that the vertex-stability and vertex-covering numbers of a graph G sum to the number of vertices of G (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 3 , May 1978 , pp. 347 - 351
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

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