✦ LIBER ✦

A construction for binary matroids

✍ Scribed by Francisco Barahona; Michele Conforti

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 384 KB
Volume: 66
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90097-5

No coin nor oath required. For personal study only.

✦ Synopsis

A family of subsets of a ground set closed under the operation of taking symmetric differences is the family of cycles of a binary matroid. Its circuits are the minimal members of this collection. We use this basic property to derive binary matroids from binary matroids. In particular, we derive two matroids from graphic and cographic matroids. Cocycles of the first one are cutsets or balancing sets. Coeycles of the second one are Eulerian subgraphs or T-joins. We study the problem of finding a minimum weight circuit and cocirenit in these matroids.

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