Eigenvalues and the max-cut problem

Bojan Mohar; Svatopluk Poljak

Czechoslovak Mathematical Journal (1990)

  • Volume: 40, Issue: 2, page 343-352
  • ISSN: 0011-4642

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Mohar, Bojan, and Poljak, Svatopluk. "Eigenvalues and the max-cut problem." Czechoslovak Mathematical Journal 40.2 (1990): 343-352. <http://eudml.org/doc/13856>.

@article{Mohar1990,
author = {Mohar, Bojan, Poljak, Svatopluk},
journal = {Czechoslovak Mathematical Journal},
keywords = {max-cut problem; Laplacian eigenvalues; Kneser graphs; circulants; Ramanujan graphs},
language = {eng},
number = {2},
pages = {343-352},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Eigenvalues and the max-cut problem},
url = {http://eudml.org/doc/13856},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Mohar, Bojan
AU - Poljak, Svatopluk
TI - Eigenvalues and the max-cut problem
JO - Czechoslovak Mathematical Journal
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 2
SP - 343
EP - 352
LA - eng
KW - max-cut problem; Laplacian eigenvalues; Kneser graphs; circulants; Ramanujan graphs
UR - http://eudml.org/doc/13856
ER -

References

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  1. N. Alon, 10.1007/BF02579166, Combinatorica 6, (1986) 83-96. (1986) Zbl0661.05053MR0875835DOI10.1007/BF02579166
  2. N. Alon V. D. Milman, 10.1016/0095-8956(85)90092-9, J. Comb. Th. B 38 (1985) 73-88. (1985) Zbl0549.05051MR0782626DOI10.1016/0095-8956(85)90092-9
  3. W. N. Anderson T. D. Morley, 10.1080/03081088508817681, Lin. Multilin. Algebra 18 (1985) 141-145. (1985) Zbl0594.05046MR0817657DOI10.1080/03081088508817681
  4. F. Barahona, 10.1016/0167-6377(83)90016-0, Oper. Res. Lett. 2 (1983) 107-111. (1983) Zbl0525.90094MR0717742DOI10.1016/0167-6377(83)90016-0
  5. F. Barahona M. Grötschel M. Jünger G. Reinelt, 10.1287/opre.36.3.493, Oper. Res. 36 (1988) 493-513. (1988) Zbl0646.90084DOI10.1287/opre.36.3.493
  6. D. M. Cvetkovic M. Doob, and H. Sachs, Spectra of graphs - Theory and applications, VEB Deutscher Verlag der Wiss. Berlin 1979/Acad. Press, N.Y. 1979. (1979) Zbl0824.05046
  7. M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (98) (1973) 298-305. (1973) Zbl0265.05119MR0318007
  8. M. Grötschel, G. L. Nemhauser, 10.1007/BF02591727, Math. Programming 29 (1984) 28-40. (1984) Zbl0532.90074MR0740503DOI10.1007/BF02591727
  9. M. Grötschel, W. R. Pulleyblank, 10.1016/0167-6377(81)90020-1, Oper. Res.Lett. / (1981) 23-27. (1981) Zbl0494.90078MR0643056DOI10.1016/0167-6377(81)90020-1
  10. F. Hadlock, 10.1137/0204019, SIAM J. on Comp. 4 (1975) 221-225. (1975) Zbl0321.05120MR0379290DOI10.1137/0204019
  11. R. M. Karp, Reducibility among combinatorial problems, in Complexity of Computer Computations, R. E. Miller, J. W. Thatcher (eds.), Plenum Press, New York 1972, pp. 85-103. (1972) Zbl0366.68041MR0378476
  12. A. K. Kel'mans, Properties of the characteristic polynomial of a graph, "Kibernetiky - na službu kommunizmu" vol. 4, Energija, Moskva-Leningrad, 1967, pp. 27-41 (in Russian). (1967) MR0392633
  13. P. Lankaster, Theory of Matrices, Acad. Press, New York-London 1969. (1969) MR0245579
  14. L. Lovász, 10.1109/TIT.1979.1055985, IEEE Trans. Inform. Theory 25 (1979) 1-7. (1979) Zbl0395.94021MR0514926DOI10.1109/TIT.1979.1055985
  15. A. Lubotzky R. Phillips, P. Sarnak, 10.1007/BF02126799, Combinatorica, 8 (1988) 261-277. (1988) Zbl0661.05035MR0963118DOI10.1007/BF02126799
  16. B. Mohar, Isoperimetric numbers of graphs, J. Comb. Th. B, to appear. Zbl0719.05042MR1026065
  17. B. Mohar, The Laplacian spectrum of graphs, submitted. Zbl0840.05059
  18. J. Nešetřil, S. Poljak, 10.1016/0167-6377(86)90031-3, Oper. Res. Lett. 4 (1986) 289-291. (1986) Zbl0585.90085MR0836264DOI10.1016/0167-6377(86)90031-3
  19. G. I. Orlova, Y. G. Dorfman, Finding the maximal cut in a graph, Engrg. Cybernetics 10 (1972) 502-506. (1972) Zbl0247.05151MR0329962
  20. S. Poljak, Z. Tuza, 10.1007/BF01788540, Graphs and Combinatorics, 3 (1987) 191-199. (1987) Zbl0674.05064MR0932133DOI10.1007/BF01788540
  21. S. Poljak, D. Turzík, 10.1016/0012-365X(86)90192-5, Discrete Math. 58 (1986) 99-104. (1986) Zbl0585.05032MR0820844DOI10.1016/0012-365X(86)90192-5
  22. S. Poljak, D. Turzík, Maximum bipartite subgraphs of circulants, submitted. Zbl0471.68041
  23. R. M. Tanner, 10.1137/0605030, SIAM J. Alg. Disc. Meth. 5 (1984) 287-293. (1984) Zbl0554.05045MR0752035DOI10.1137/0605030

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