F.B. Shepherd, Applying Lehman's theorems to packing problems, Mathematical Programming, 71 (1995), 353-367. Home/Search Document Details and Download
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Rank-Perfect and Weakly Rank-Perfect Graphs - Wagler (Correct)
....edges of F are incident) see Section 2 and Section 3 for more details. As a natural generalization of rank perfect graphs, we analogously de ne graphs G with WSTAB(G) STAB(G) to be weakly rank perfect. Two graph classes are known to consist of weakly rank perfect graphs due to Shepherd [12]: near bipartite graphs and complements of line graphs. A graph G is near bipartite if G N(v) can be partitioned into two stable sets for all nodes v of G, i.e, if removing all neighbors of an arbitrary node leaves the graph bipartite) The class of near bipartite graphs contains all complements ....
....node 6, we have to choose lifting coecient a 6 = 2. The resulting facet x(C 5 ; 1l) 2x 6 2 of STAB(G) is a special weak rank constraint, called odd wheel constraint x(C 2k 1 ; 1l) kx c k (3a) where c is the central node adjacent to all nodes of the odd hole C 2k 1 and k 2. Shepherd [12] studied a more general weak rank constraint X i k 1 (W i ) x(W i ) x(Q; 1l) 1 (3b) 6 associated with the complete join of prime antiwebs W 1 ; W k and a clique Q and showed that the stable set polytope of near bipartite graphs have facets of type (3b) as only nontrivial ....
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F.B. Shepherd, Applying Lehman's Theorem to Packing Problems. Math. Programming 71 (1995) 353-367
Integer Polyhedra: Combinatorial Properties and Complexity - Sebö (2001) (Correct)
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F.B. Shepherd, Applying Lehman's theorems to packing problems, Mathematical Programming, 71 (1995), 353-367.
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