Quasi-random hypergraphs and spanning subhypergraph containment

• Grant number: 10/16526-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2011
• End date: March 07, 2015
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Yoshiharu Kohayakawa
• Grantee: Hiep Han
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 13/11353-1 - Degenerate extremal problems for random discrete structures, BE.EP.PD

Abstract

This is a research proposal submitted to FAPESP for Hiêp Hàn's application for a postdoctoral fellowship at the Institute of Mathematics and Statistics of the University of São Paulo (IME/USP). Hàn's stay in São Paulo is initially planned for 24 months, from 4 January 2011. This researcher will be a member of the combinatorics and theory group at IME/USP and of NUMEC, Núcleo de Modelagem Estocástica e Complexidade, a research centre of USP.The main themes of the proposed research are quasi-randomness of graphs and hypergraphs, and extremal problems for hypergraphs. More specifically, problems along three lines of research are proposed: (i) weak notions of quasi-randomness for hypergraphs and applications, (ii) quasi-randomness for sparse structures, including graphs with given degree sequences and (iii) extremal problems for spanning subhypergraphs, such as Hamilton cycles. Several of the proposed problems involving quasi-randomness suggest accompanying regularity lemmas and applications.

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HAN, HIEP; RETTER, TROY; ROEDL, VOJTECH; SCHACHT, MATHIAS. amsey-type numbers involving graphs and hypergraphs with large girt. COMBINATORICS PROBABILITY & COMPUTING, v. 30, n. 5, p. 722-740, SEP 2021. (10/16526-3, 13/11353-1)

BUSS, ENNO; HAN, HIEP; SCHACHT, MATHIAS. Minimum vertex degree conditions for loose Hamilton cycles in 3-uniform hypergraphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 103, n. 6, p. 658-678, NOV 2013. (10/16526-3)

ALLEN, PETER; BOTTCHER, JULIA; HAN, HIEP; KOHAYAKAWA, YOSHIHARU; PERSON, YURY. POWERS OF HAMILTON CYCLES IN PSEUDORANDOM GRAPHS. COMBINATORICA, v. 37, n. 4, p. 573-616, AUG 2017. (10/16526-3, 09/17831-7, 13/07699-0, 10/09555-7, 13/03447-6)

ALLEN, PETER; BOETTCHER, JULIA; HAN, HIEP; KOHAYAKAWA, YOSHIHARU; PERSON, YURY; PARDO, A; VIOLA, A. Powers of Hamilton Cycles in Pseudorandom Graphs. LATIN 2014: THEORETICAL INFORMATICS, v. 8392, p. 12-pg., 2014-01-01. (09/17831-7, 13/07699-0, 10/16526-3, 13/03447-6, 10/09555-7)

GAUY, MARCELO M.; HAN, HIEP; OLIVEIRA, IGOR C.. Erdos-Ko-Rado for Random Hypergraphs: Asymptotics and Stability. COMBINATORICS PROBABILITY & COMPUTING, v. 26, n. 3, p. 406-422, MAY 2017. (13/11353-1, 10/16526-3)

AIGNER-HOREV, ELAD; HAN, HIEP. Polynomial configurations in subsets of random and pseudo-random sets. JOURNAL OF NUMBER THEORY, v. 165, p. 363-381, AUG 2016. (13/11353-1, 10/16526-3)

AIGNER-HOREV, ELAD; HAN, HIEP; SCHACHT, MATHIAS. Extremal results for odd cycles in sparse pseudorandom graphs. COMBINATORICA, v. 34, n. 4, p. 379-406, AUG 2014. (10/16526-3)