“Ramsey Theorem and Turán extremal graph theorem are both among the basic theorems of graph theory. Both served as starting points of whole branches in graph theory and both are applied in many fields of mathematics. In the late 1960s a whole new theory emerged, connecting these fields problems” (by M. Simonovot, V.T. Sós).
We introduced and studied a new class of Ramsey-Turán problems. In ref. 1, we conjectured that if G is a graph of sufficiently large order n with minimum degree δ( G) >3n/4 such that the edges of G are colored in blue or red, then for all integer k between 4 and n/2 , there exists a monochromatic cycle of length k. We proved that the conjecture is true for all integer k between 4 and (1/8-ε) n.
In this proposal of a PhD dissertation, we continue to study the above conjecture. We also work on many related problems in this type.
Ref.
1.H. Li, V. Nikiforov and R.H. Schelp, A new class of Ramsey-Turán problems
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graph theory, combinatorics
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Hao.Li
Créé
Mardi 15 janvier 2013 17:46:35 CET
dernière modif.
Mardi 15 janvier 2013 17:46:35 CET
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Ecole Doctorale Informatique Paris-Sud
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Nicole Bidoit Assistante
Stéphanie Druetta Conseiller aux thèses
Dominique Gouyou-Beauchamps
ED 427 - Université Paris-Sud
UFR Sciences Orsay
Bat 650 - aile nord - 417
Tel : 01 69 15 63 19
Fax : 01 69 15 63 87
courriel: ed-info à lri.fr