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2012 | 32 | 2 | 279-287
Tytuł artykułu

On kaleidoscopic pseudo-randomness of finite Euclidean graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
D. Hart, A. Iosevich, D. Koh, S. Senger and I. Uriarte-Tuero (2008) showed that the distance graphs has kaleidoscopic pseudo-random property, i.e. sufficiently large subsets of d-dimensional vector spaces over finite fields contain every possible finite configurations. In this paper we study the kaleidoscopic pseudo-randomness of finite Euclidean graphs using probabilistic methods.
Wydawca
Rocznik
Tom
32
Numer
2
Strony
279-287
Opis fizyczny
Daty
wydano
2012
otrzymano
2008-09-15
poprawiono
2011-05-11
zaakceptowano
2011-05-23
Twórcy
autor
  • Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, Vietnam National University, Hanoi
Bibliografia
  • [1] N. Alon and J.H. Spencer, The Probabilistic Method (Willey-Interscience, 2000).
  • [2] E. Bannai, O. Shimabukuro and H. Tanaka, Finite Euclidean graphs and Ramanujan graphs, Discrete Math. 309 (2009) 6126-6134, doi: 10.1016/j.disc.2009.06.008.
  • [3] D. Hart, A. Iosevich, D. Koh, S. Senger and I. Uriarte-Tuero, Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness preprint, arXiv:0804.3036v1.
  • [4] A. Iosevich and M. Rudnev, Erdös distance problem in vector spaces over finite fields, Trans. Amer. Math. Soc. 359 (2007) 6127-6142, doi: 10.1090/S0002-9947-07-04265-1.
  • [5] M. Krivelevich and B. Sudakov, Pseudo-random graphs, in: Conference on Finite and Infinite Sets Budapest, Bolyai Society Mathematical Studies X, (Springer, Berlin 2006) 1-64.
  • [6] S. Li and L.A. Vinh, On the spectrum of unitary finite-Euclidean graphs, Ars Combinatoria, to appear.
  • [7] A. Medrano, P. Myers, H.M. Stark and A. Terras, Finite analogues of Euclidean space, Journal of Computational and Applied Mathematics 68 ( 1996) 221-238, doi: 10.1016/0377-0427(95)00261-8.
  • [8] L.A. Vinh and D.P. Dung, Explicit tough Ramsey graphs, in: Proceedings of the International Conference on Relations, Orders and Graphs: Interaction with Computer Science, ( Nouha Editions, 2008) 139-146.
  • [9] L.A. Vinh, Explicit Ramsey graphs and Erdös distance problem over finite Euclidean and non-Euclidean spaces, Electronic J. Combin. 15 (2008) R5.
  • [10] L.A. Vinh, Szemeredi-Trotter type theorem and sum-product estimate in finite fields, European J. Combin., to appear.
  • [11] V. Vu, Sum-product estimates via directed expanders, Mathematical Research Letters, 15 (2008) 375-388.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1597
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