By Alexander Schrijver

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4b Ideality is in co-NP . . . . . . . . . . . . . . . 5 Further results and notes . . . . . . . . . . . . . . . 5a Composition of clutters . . . . . . . . . . . . . 5b Further notes . . . . . . . . . . . . . . . . . 1392 1394 1395 1395 1395 79 Mengerian hypergraphs . . . . . . . . . . . . . . . . . 1 Mengerian hypergraphs . . . . . . . . . . . . . . . . 1a Examples of Mengerian hypergraphs . . . . . . .

4a Lov´asz’s proof of the replication lemma . . . . . . 5 Decomposition of Berge graphs . . . . . . . . . . . . . 5a 0- and 1-joins . . . . . . . . . . . . . . . . . 5b The 2-join . . . . . . . . . . . . . . . . . . . 6 Pre-proof work on the strong perfect graph conjecture . . . 6a Partitionable graphs . . . . . . . . . . . . . . 6b More characterizations of perfect graphs . . . . . . 6c The stable set polytope of minimally imperfect graphs .

The content of Edmonds’ theorem is the converse inclusion. This will be proved in Chapter 25. In fact, Edmonds designed a polynomial-time algorithm to find a maximum-weight matching in a graph, which gave this polyhedral characterization as a by-product. Conversely, from the characterization one may derive the polynomial-time solvability of the weighted matching problem, with the ellipsoid method. In applying linear programming methods for this, one will be faced with the fact that the system Ax ≤ b consists of exponentially many inequalities, since there exist exponentially many odd-size subsets U of V .

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