论文信息 - Relaxations of vertex packing

Relaxations of vertex packing

Abstract A polynomially computable upper bound for the weighted independence number of a graph is studied. This gives rise to a convex body containing the vertex packing polytope of the graph. This body is a polytope if and only if the graph is perfect. As an application of these notions, we show that the maximum weight independent set of an h -perfect graph can be found in polynomial time.

[1] D. R. Fulkerson. On the Perfect Graph Theorem , 1973 .

[2] M. Golumbic. Algorithmic graph theory and perfect graphs , 1980 .

[3] Mouloud Boulala,et al. Polytope des independants d'un graphe serie-parallele , 1979, Discret. Math..

[4] V. Chvátal. On certain polytopes associated with graphs , 1975 .

[5] László Lovász,et al. On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[6] L. Lovász,et al. Polynomial Algorithms for Perfect Graphs , 1984 .

[7] J. P. Uhry,et al. Transformations which Preserve Perfectness and H-Perfectness of Graphs , 1982 .

[8] László Lovász,et al. Normal hypergraphs and the perfect graph conjecture , 1972, Discret. Math..

[9] Martin Grötschel,et al. The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[10] D. R. Fulkerson,et al. Blocking and anti-blocking pairs of polyhedra , 1971, Math. Program..

[11] Bert Gerards,et al. Matrices with the edmonds—Johnson property , 1986, Comb..