Embedding, randomised and structural problems in extremal graph theory

• Grant number: 10/09555-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2010
• End date: December 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Yoshiharu Kohayakawa
• Grantee: Peter David Allen
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This is a proposal for a postdoctoral fellowship for Peter David Allen, to be held at the Institute of Mathematics and Statistics of the University of São Paulo (IME/USP), from 6 September 2010, initially proposed for 24 months. 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.Research in four directions in extremal graph theory is proposed: (i) extremal conditions for the existence of large subgraphs, (ii) randomised restrictions in extremal combinatorics, (iii) progress towards a regularity-free embedding method, (iv) structural and limits theory for dense K_{s,t}-free graphs.

Scientific publications

(13)

(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)

ALLEN, PETER; BOTTCHER, JULIA; COOLEY, OLIVER; MYCROFT, RICHARD. Tight cycles and regular slices in dense hypergraphs. JOURNAL OF COMBINATORIAL THEORY SERIES A, v. 149, p. 30-100, JUL 2017. (10/09555-7, 09/17831-7)

ALLEN, PETER; BOTTCHER, JULIA; GRIFFITHS, SIMON; KOHAYAKAWA, YOSHIHARU; MORRIS, ROBERT. Chromatic Thresholds in Sparse Random Graphs. RANDOM STRUCTURES & ALGORITHMS, v. 51, n. 2, p. 215-236, SEP 2017. (09/17831-7, 13/07699-0, 13/03447-6, 10/09555-7)

ALLEN, PETER; BOETTCHER, JULIA; PERSON, YURY. An improved error term for minimum H-decompositions of graphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 108, p. 92-101, SEP 2014. (09/17831-7, 10/09555-7)

ALLEN, P.; KOHAYAKAWA, Y.; MOTA, G. O.; PARENTE, R. F.. On the number of orientations of random graphs with no directed cycles of a given length. ELECTRONIC JOURNAL OF COMBINATORICS, v. 21, n. 1, MAR 10 2014. (13/07699-0, 10/09555-7, 12/00036-2, 13/03447-6, 13/20733-2, 09/06294-0)

ALLEN, PETER; BOETTCHER, JULIA; HLADKY, JAN; PIGUET, DIANA. Turannical hypergraphs. RANDOM STRUCTURES & ALGORITHMS, v. 42, n. 1, p. 29-58, JAN 2013. (09/17831-7, 10/09555-7)

ALLEN, PETER; BOTTCHER, JULIA; GRIFFITHS, SIMON; KOHAYAKAWA, YOSHIHARU; MORRIS, ROBERT. Chromatic Thresholds in Dense Random Graphs. RANDOM STRUCTURES & ALGORITHMS, v. 51, n. 2, p. 185-214, SEP 2017. (13/03447-6, 09/17831-7, 10/09555-7, 13/07699-0)

ALLEN, PETER; BOETTCHER, JULIA; HLADKY, JAN; PIGUET, DIANA. A Density Corradi-Hajnal Theorem. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, v. 67, n. 4, p. 721-758, AUG 2015. (09/17831-7, 10/09555-7)

ALLEN, PETER; BOETTCHER, JULIA; HLADKY, JAN; PIGUET, DIANA. An extension of Turan's Theorem, uniqueness and stability. ELECTRONIC JOURNAL OF COMBINATORICS, v. 21, n. 4, OCT 2 2014. (09/17831-7, 10/09555-7)

ALLEN, PETER; KEEVASH, PETER; SUDAKOV, BENNY; VERSTRAETE, JACQUES. Turan numbers of bipartite graphs plus an odd cycle. JOURNAL OF COMBINATORIAL THEORY SERIES B, v. 106, p. 134-162, MAY 2014. (10/09555-7)

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; KOHAYAKAWA, YOSHIHARU; PERSON, YURY. Tight Hamilton Cycles in Random Hypergraphs. RANDOM STRUCTURES & ALGORITHMS, v. 46, n. 3, p. 446-465, MAY 2015. (09/17831-7, 13/07699-0, 13/03447-6, 10/09555-7)

ALLEN, PETER; BOETTCHER, JULIA; GRIFFITHS, SIMON; KOHAYAKAWA, YOSHIHARU; MORRIS, ROBERT. The chromatic thresholds of graphs. ADVANCES IN MATHEMATICS, v. 235, p. 261-295, MAR 1 2013. (09/17831-7, 10/09555-7)

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)