Quadratic forms on graphs

Inventiones Mathematicae

Volumn 163, Issue 3, 2006, Pages 499-522

  Alon, Noga ^a,b   Makarychev, Konstantin ^c   Makarychev, Yury ^c   Naor, Assaf ^d  

^a TEL AVIV UNIVERSITY   (Israel)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

^c Princeton University   (United States)

^d MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32144451020     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-005-0465-9     Document Type: Review

References (27)

1. Alon, N.: Explicit Ramsey graphs and orthonormal labelings. Electron. J. Comb, 1, R12 (1994)
2. Alon, N.: Covering a hypergraph of subgraphs. Discrete Math. 257, 249-254 (2002)
3. th ACM STOC, pp. 72-80, 2004
4. Alon, N., Gutin, G., Krivelevich, M.: Algorithms with large domination ratio. J. Algorithms 50, 118-131 (2004)
5. Alon, N., Orlitsky, A.: Repeated communication and Ramsey graphs: IEEE Trans. Inf. Theory 41, 1276-1289 (1995)
6. Bansal, N., Slum, A., Chowla, S.: Correlation Clustering. Proc. of the 43 IEEE FOCS, pp. 238-247, 2002
7. Barahona, F.: On the computational complexity of Ising spin glass models. J. Phys. A, Math. Gen. 15, 3241-3253 (1982)
8. p(G). Ann. Inst. Fourier 20, 335-402 (1970)
9. Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. Proc. of the 44 IEEE FOCS, pp. 524-533, 2003
10. Charikar, M., Wirth, A.: Maximizing quadratic programs: extending Grothendieck's Inequality, pp. 54-60. FOCS 2004
11. Ding, G., Seymour, P.D., Winkler, P.: Bounding the vertex cover number of a hypergraph. Combinatorica 14, 23-34 (1994)
12. Frieze, A.M., Kannan, R.: Quick Approximation to matrices and applications. Combinatorica 19, 175-200 (1999)
13. Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 169-197 (1981)
14. Grothendieck, A.: Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. Sao Paolo 8, 1-79 (1953)
15. Johnson, W.B., Lindenstrauss, J.: Basic concepts in the geometry of Banach spaces. Handbook of the geometry of Banach spaces, vol. I, pp. 1-84. Amsterdam: North-Holland 2001
16. Juhász, F.: The asymptotic behaviour of Lovász' θ function for random graphs. Combinatorica 2, 153-155 (1982)
17. Kim, S.-J., Kostochka, A., Nakprasit, K.: On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane. Electron. J. Comb. 11, R52 (2004)
18. Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semidefinite programming. J. ACM 45, 246-265 (1998)
19. Kashin, B.S., Szarek, S.J.: On the Gram Matrices of Systems of Uniformly Bounded Functions. Proc. Steklov Inst. Math., vol. 243, pp. 227-233, 2003
20. Krivine, J.: Sur la constante de Grothendieck. C. R. Acad. Sci., Paris, Sér. A-B 284, 445-446 (1977)
21. p spaces and their applications. Studia Math. 29, 275-326 (1968)
22. Lovász, L.: Kneser's conjecture, chromatic number and homotopy, J. Comb. Theory 25, 319-324 (1978)
23. Lovász, L.: On the Shannon capacity of agraph. IEEE Trans. Inf. Theory 25, 1-7 (1979)
24. Lovász, L., Plummer, M.D.: Matching Theory. Amsterdam: North Holland 1986
25. Megretski, A.: Relaxation of Quadratic Programs in Operator Theory and System Analysis. In: Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), pp. 365-392. Basel: Birkhäuser 2001
26. Nemirovski, A., Roos, C., Terlaky, T.: On Maximization of Quadratic Form over Intersection of Ellipsoids with Common Center. Math. Program. 86, 463-473 (1999)
27. Talagrand, M.: Spin glasses: a challenge for mathematicians. Cavity and mean field models, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, 46. Berlin: Springer 2003