Bonn Workshop on Combinational Optimization: Lectures by Achim Bachem, etc.

By Achim Bachem, etc.

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2 (1972) 253-267. 1111 H. Meyniel, On the perfect graph conjecture, Discrete Math. 16 (1976) 339-342. J. Minty, On maximal independent sets of vertices in claw-free graphs, J. Combin. Theory Ser. B 28 (1980) 284-304. [13] H. Sachs, On the Berge conjecture concerning perfect graphs, in: Combinatorid Structures and their Applications (Gordon and Breach, New York, 1970) pp. 377-384. 26 M. P. Uhry [14] L. SurAnyi, The covering of graphs by cliques, Studia Sci. Math. Hungar. 3 (1968) 345-349. C. Tucker, The strong perfect graph conjecture for planar graphs, Canad.

2] M. P. Uhry, Polytopes des indkpendants d’un graphe serie-parall&le, Discrete Math. 27 (1979) 225-243. G. Corneil, H. Lerchs and L. Stewart, Cographs: a new class of perfect graphs, Discrete Appl. , t o appear. R. R. Fulkerson, Flows in Networks (Princeton University Press, Princeton, 1962). [5] T. Gallai, Graphen mit triangulierbaren ungeraden Vielecken, Magyar Tud. Akad. Mat. Kutato Int. Kozl. A 7 (1%2) 3-36. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).

In fact an inequality can always be replaced by another obtained by multiplying by a positive constant and adding any linear combination of the equations which define the affine space containing the polytope. Generally, full dimensional polytopes seem more pleasant to handle, so what is often done when studying the travelling salesman polytope is to consider, in fact, the SO called monotone trauelling salesman polytope: the convex hull of the incidence vectors of the hamilton cycles and all subsets of hamilton cycles of a graph.

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