Hanani triple systems
type: Item
instance of: scholarly article
title: Hanani triple systems
zbMATH Open document ID: 0783.05023
DOI: 10.1007/BF02784058
author: M. C. Fu
published in: Israel Journal of Mathematics
publication date: 1993-12-07T00:00:00Z
review text: Hanani triple systems on \(v \equiv 1 \pmod 6\) elements are Steiner triple systems having \((v-1)/2\) pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that span \(v-1\) elements), and the remaining triples form a parallel class. Hanani triple systems are one natural analogue of the Kirkman triple systems on \(v \equiv 3 \pmod 6\) elements, which form the solution of the celebrated Kirkman schoolgirl problem. The authors prove that a Hanani triple system exists for all \(v \equiv 1 \pmod 6\) except for \(v \in \{7,13\}\). This result has many applications in design constructions (e.g., for almost resolvable twofold triple systems), and suggests a number of generalizations and open problems, especially on minimum chromatic index of designs.
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 446876
zbMATH Keywords: Hanani triple system
zbMATH Keywords: Steiner triple systems
zbMATH Keywords: parallel class
zbMATH Keywords: Kirkman triple systems
Wikidata QID: Q106038903
reviewed by: Jozef Širáň
MaRDI profile type: Publication
cites work: Q3794196
cites work: The chromatic index of cyclic Steiner 2-designs
cites work: Greedy Colourings of Steiner Triple Systems
cites work: Q4026147
cites work: Q3715120
cites work: On resolvable balanced incomplete block designs
cites work: Q4068738
cites work: Steiner Systems and Room Squares
cites work: Asymptotic behavior of the chromatic index for hypergraphs
cites work: Q5661892
cites work: Q3757923
cites work: Q4026152
cites work: Frames for Kirkman triple systems
full work available at URL: https://doi.org/10.1007/bf02784058
OpenAlex ID: W2020891528
description: scientific article; zbMATH DE number 446876