List of issues > Series «Mathematics». 2007. Vol. 1
Two quadratic problems for estimating and searching a maximum clique
We consider the maximum clique problem and its formulation as two continuous problems. Using these continuous formulations some upper bounds for the maximum clique cardinality are obtained. The parameter variation segment is received as well.
1. Васильев Ф.П. Численные методы решения экстремальных задач. — М.: Наука, 1988.
2. Кузнецова А.А., Карпачева О.Н. Два метода локального поиска с параметрами для задачи о максимальной клике // Методы оптимизации и их приложения.: Тр. Междунар. конф. — Иркутск: ИСЭМ СО РАН, 2005. — Т. 1. — С. 527–533.
3. Bomze I. Evolution towards the maximum clique // J. of Global Optimization. — 1997. — V. 10. — P. 143–164.
4. Bomze I.M., Budinich M., Pardalos P.M., Pelillo, M. The maximum clique problem // Handbook of Combinatorial Optimization. /Ed. by D.-Z. Du , P.M. Pardalos. — Kluwer, 1999. — Suppl. Vol. A. — P. 1–74.
5. Kuznetsova A., Strekalovsky A.S. On solving the maximum clique problem // J. of Global Optimization. — 2001. — V. 21, N. 3. — P. 265–288.
6. Motzkin T.S., Straus, E.G., Maxima for graphs and a new proof of a theorem of Tur´an // Canad. J. Math. — 1965. — V. 17. — P. 533–540.
7. Pardalos P.M. Continuous approaches to discrete optimization problems // Nonlinear Optimization and Applications/ Eds. by G.Di. Pillo and F. Giannessi. — New York: Plenum Press, 1996. — P. 313–328.
8. Wilf H. S. The eigenvalues of a graph and its chromatic number //J. London Math. Soc. — 1967. — Vol. 42. — P. 330–332.