Hamilton cycles and tiling problems in hypergraphs

• Grant number: 14/18641-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2015
• End date: August 18, 2018
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Yoshiharu Kohayakawa
• Grantee: Jie Han
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science, AP.TEM
• Associated scholarship(s): 15/07869-8 - Perfect matchings and Tilings in hypergraphs, BE.EP.PD

Abstract

This is the research project for Jie Han's postdoctoral fellowship at the Institute of Mathematics and Statistics of the University of São Paulo (IME/USP). This researcher will be a member of the combinatorics and theory group of IME/USP, and he wil also be a member of NUMEC, Núcleo de Modelagem Estocástica e Complexidade, a research centre of the University of São Paulo.We propose to investigate two classes of problems in graph and hypergraph theory together with a collection of other related extremal problems. We propose to attack problems in the following lines of research: (i) Hamilton cycles in hypergraphs with degree conditions, (ii) tiling problems for hypergraph with degree conditions and (iii) general spanning substructures in pseudorandom graphs and hypergraphs.

Scientific publications

(28)

(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, JIE. DECISION PROBLEM FOR PERFECT MATCHINGS IN DENSE k-UNIFORM HYPERGRAPHS. Transactions of the American Mathematical Society, v. 369, n. 7, p. 5197-5218, JUL 2017. (14/18641-5, 15/07869-8)

BASTOS, JOSEFRAN DE OLIVEIRA; BENEVIDES, FABRICIO SIQUEIRA; HAN, JIE. The number of Gallai k-colorings of complete graphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 144, p. 1-13, SEP 2020. (14/18641-5)

HAN, JIE; LO, ALLAN; SANHUEZA-MATAMALA, NICOLAS. Covering and tiling hypergraphs with tight cycles. COMBINATORICS PROBABILITY & COMPUTING, v. 30, n. 2, p. 288-329, MAR 2021. (14/18641-5, 13/03447-6, 15/07869-8)

HAN, JIE; ZANG, CHUANYUN; ZHAO, YI. Matchings in k-partite k-uniform hypergraphs. JOURNAL OF GRAPH THEORY, v. 95, n. 1, NOV 2019. (15/07869-8, 13/03447-6, 14/18641-5)

HAN, JIE; ZANG, CHUANYUN; ZHAO, YI. Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs. JOURNAL OF COMBINATORIAL THEORY SERIES A, v. 149, p. 115-147, JUL 2017. (14/18641-5, 13/03447-6, 15/07869-8)

FRANKL, PETER; HAN, JIE; HUANG, HAO; ZHAO, YI. A degree version of the Hilton-Milner theorem. JOURNAL OF COMBINATORIAL THEORY SERIES A, v. 155, p. 493-502, APR 2018. (14/18641-5, 13/03447-6)

HAN, JIE; LO, ALLAN; TREGLOWN, ANDREW; ZHAO, YI. Exact Minimum Codegree Threshold for K-4(-)-Factors. COMBINATORICS PROBABILITY & COMPUTING, v. 26, n. 6, p. 856-885, NOV 2017. (14/18641-5, 13/03447-6)

CHEN, GUANTAO; HAN, JIE; SUIL, O.; SHAN, SONGLING; TSUCHIYA, SHOICHI. Forbidden Pairs and the Existence of a Spanning Halin Subgraph. GRAPHS AND COMBINATORICS, v. 33, n. 5, p. 1321-1345, SEP 2017. (14/18641-5, 15/07869-8)

HAN, JIE; KOHAYAKAWA, YOSHIHARU. THE MAXIMUM SIZE OF A NON-TRIVIAL INTERSECTING UNIFORM FAMILY THAT IS NOT A SUBFAMILY OF THE HILTON-MILNER FAMILY. Proceedings of the American Mathematical Society, v. 145, n. 1, p. 73-87, JAN 2017. (15/07869-8, 14/18641-5, 13/07699-0, 13/03447-6)

HAN, JIE. On vertex-disjoint paths in regular graphs. ELECTRONIC JOURNAL OF COMBINATORICS, v. 25, n. 2, APR 27 2018. (13/03447-6, 14/18641-5)

HAN, JIE; ZHAO, YI. Forbidding Hamilton cycles in uniform hypergraphs. JOURNAL OF COMBINATORIAL THEORY SERIES A, v. 143, p. 107-115, OCT 2016. (15/07869-8, 14/18641-5)

HAN, JIE. PERFECT MATCHINGS IN HYPERGRAPHS AND THE ERDOS MATCHING CONJECTURE. SIAM JOURNAL ON DISCRETE MATHEMATICS, v. 30, n. 3, p. 1351-1357, 2016. (14/18641-5, 15/07869-8)

GAO, WEI; HAN, JIE. Minimum Codegree Threshold for C-6(3)-Factors in 3-Uniform Hypergraphs. COMBINATORICS PROBABILITY & COMPUTING, v. 26, n. 4, p. 536-559, JUL 2017. (14/18641-5, 15/07869-8, 13/03447-6)

HAN, JIE; KOHAYAKAWA, YOSHIHARU; PERSON, YURY. ear-perfect clique-factors in sparse pseudorandom graph. COMBINATORICS PROBABILITY & COMPUTING, v. 30, n. 4, p. 570-590, JUL 2021. (18/04876-1, 13/03447-6, 14/18641-5)

HAN, JIE; KOHAYAKAWA, YOSHIHARU; SALES, MARCELO TADEU; STAGNI, HENRIQUE; BENDER, MA; FARACHCOLTON, M; MOSTEIRO, MA. Property Testing for Point Sets on the Plane. LATIN 2018: THEORETICAL INFORMATICS, v. 10807, p. 13-pg., 2018-01-01. (13/07699-0, 15/15986-4, 14/18641-5, 13/03447-6)

HAN, JIE; KOHAYAKAWA, YOSHIHARU; MORRIS, PATRICK; PERSON, YURY. Finding any given 2-factor in sparse pseudorandom graphs efficiently. JOURNAL OF GRAPH THEORY, v. 96, n. 1, SI, MAY 2020. (13/03447-6, 14/18641-5)

HAN, JIE; KOHAYAKAWA, YOSHIHARU; MORRIS, PATRICK; PERSON, YURY. Clique-factors in sparse pseudorandom graphs. EUROPEAN JOURNAL OF COMBINATORICS, v. 82, DEC 2019. (13/03447-6, 14/18641-5)

HAN, JIE; TREGLOWN, ANDREW. The complexity of perfect matchings and packings in dense hypergraphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 141, p. 72-104, MAR 2020. (13/03447-6, 15/07869-8, 14/18641-5)

HAN, JIE; KOHAYAKAWA, YOSHIHARU. On hypergraphs without loose cycles. DISCRETE MATHEMATICS, v. 341, n. 4, p. 946-949, APR 2018. (14/18641-5, 13/07699-0, 13/03447-6)

BEDENKNECHT, WIEBKE; HAN, JIE; KOHAYAKAWA, YOSHIHARU; MOTA, GUILHERME O.. Powers of tight Hamilton cycles in randomly perturbed hypergraphs. RANDOM STRUCTURES & ALGORITHMS, v. 55, n. 4, JULY 2019. (14/18641-5, 13/03447-6, 18/04876-1)

GAO, WEI; HAN, JIE; ZHAO, YI. Codegree Conditions for Tiling Complete k-Partite k-Graphs and Loose Cycles. COMBINATORICS PROBABILITY & COMPUTING, v. 28, n. 6, p. 840-870, NOV 2019. (14/18641-5, 15/07869-8, 13/03447-6)

HAN, JIE; KOHAYAKAWA, YOSHIHARU; MORRIS, PATRICK; PERSON, YURY. Finding any given 2-factor in sparse pseudorandom graphs efficiently. JOURNAL OF GRAPH THEORY, v. 96, n. 1, p. 22-pg., 2020-05-05. (14/18641-5, 13/03447-6)

HAN, JIE. ON PERFECT MATCHINGS AND TILINGS IN UNIFORM HYPERGRAPHS. SIAM JOURNAL ON DISCRETE MATHEMATICS, v. 32, n. 2, p. 919-932, 2018. (13/03447-6, 14/18641-5)

HAN, JIE. NEAR PERFECT MATCHINGS IN k-UNIFORM HYPERGRAPHS II. SIAM JOURNAL ON DISCRETE MATHEMATICS, v. 30, n. 3, p. 1453-1469, 2016. (14/18641-5, 15/07869-8)

HAN, JIE; KIM, JAEHOON. Two-regular subgraphs of odd-uniform hypergraphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 128, p. 175-191, JAN 2018. (13/03447-6, 14/18641-5, 15/07869-8)

HAN, JIE; ZHAO, YI. Hamiltonicity in randomly perturbed hypergraphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 144, p. 14-31, SEP 2020. (14/18641-5)

HAN, JIE; GOPAL, TV; JAGER, G; STEILA, S. The Complexity of Perfect Packings in Dense Graphs. THEORY AND APPLICATIONS OF MODELS OF COMPUTATION (TAMC 2017), v. 10185, p. 15-pg., 2017-01-01. (14/18641-5, 15/07869-8, 13/03447-6)

HAN, JIE. DECISION PROBLEM FOR PERFECT MATCHINGS IN DENSE k-UNIFORM HYPERGRAPHS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 369, n. 7, p. 22-pg., 2017-07-01. (14/18641-5, 15/07869-8)