# On kaleidoscopic pseudo-randomness of finite Euclidean graphs

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 2, page 279-287
- ISSN: 2083-5892

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topLe Anh Vinh. "On kaleidoscopic pseudo-randomness of finite Euclidean graphs." Discussiones Mathematicae Graph Theory 32.2 (2012): 279-287. <http://eudml.org/doc/270881>.

@article{LeAnhVinh2012,

abstract = {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.},

author = {Le Anh Vinh},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {finite Euclidean graphs; kaleidoscopic pseudo-randomness},

language = {eng},

number = {2},

pages = {279-287},

title = {On kaleidoscopic pseudo-randomness of finite Euclidean graphs},

url = {http://eudml.org/doc/270881},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Le Anh Vinh

TI - On kaleidoscopic pseudo-randomness of finite Euclidean graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 2

SP - 279

EP - 287

AB - 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.

LA - eng

KW - finite Euclidean graphs; kaleidoscopic pseudo-randomness

UR - http://eudml.org/doc/270881

ER -

## References

top- [1] N. Alon and J.H. Spencer, The Probabilistic Method (Willey-Interscience, 2000). Zbl0996.05001
- [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. Zbl1208.05046
- [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. Zbl1145.11083
- [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. Zbl0874.05030
- [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. Zbl1206.05054
- [10] L.A. Vinh, Szemeredi-Trotter type theorem and sum-product estimate in finite fields, European J. Combin., to appear. Zbl1253.11015
- [11] V. Vu, Sum-product estimates via directed expanders, Mathematical Research Letters, 15 (2008) 375-388. Zbl1214.11021

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