Asymptotic enumeration of sparse uniform hypergraphs with given degrees

Author(s)

Blinovsky, Vladimir ^{[1, 2]} ; Greenhill, Catherine ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil

^[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127994 - Russia

^[3] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052 - Australia

• Document type: Journal article
• Source: EUROPEAN JOURNAL OF COMBINATORICS; v. 51, p. 287-296, JAN 2016.
• Web of Science Citations: 3

Abstract

Let r >= 2 be a fixed integer. For infinitely many n, let k = (k(1), ... , k(n)) be a vector of nonnegative integers such that their sum M is divisible by r. We present an asymptotic enumeration formula for simple r-uniform hypergraphs with degree sequence k. (Here ``simple{''} means that all edges are distinct and no edge contains a repeated vertex.) Our formula holds whenever the maximum degree k(max) satisfies k(max)(3) = o(M). (C) 2015 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Oswaldo Baffa Filho
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 12/13341-8 - Problems in extremal combinatorics
• Grantee: Yoshiharu Kohayakawa
• Support Opportunities: Research Grants - Visiting Researcher Grant - International