We define some new matroids on the edge set of a graph. We show that minimal disconnecting edge sets and minimal edge sets which cover all the odd cycles are cocircuits of a binary matroid. We give a polynomial algorithm for finding a minimum weight circuit in our matroids. A necessary and sufficient condition for an edge set to be the minimum weight odd cycle cover is derived in terms of the family of cut sets of the graph.
Some New Matroids on Graphs: Cut Sets and the Max Cut Problem
CONFORTI, MICHELANGELO;
1987
Abstract
We define some new matroids on the edge set of a graph. We show that minimal disconnecting edge sets and minimal edge sets which cover all the odd cycles are cocircuits of a binary matroid. We give a polynomial algorithm for finding a minimum weight circuit in our matroids. A necessary and sufficient condition for an edge set to be the minimum weight odd cycle cover is derived in terms of the family of cut sets of the graph.
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