Minimum embedding of a \(P_{4}\)-design into a balanced incomplete block design of index \(\lambda \)
type: Item
instance of: scholarly article
title: Minimum embedding of a \(P_{4}\)-design into a balanced incomplete block design of index \(\lambda \)
zbMATH Open document ID: 1186.05025
author: Peter Danziger
author: Salvatore Milici
author: Gaetano Quattrocchi
published in: Discrete Mathematics
publication date: 2009-12-15T00:00:00Z
review text: The problem of embedding a \(P_4\)-design of index \(\mu\) with \(v\) elements into a balanced incomplete block design of index \(\lambda\) and block size four, having \(v+w\) elements, is studied. In the case when \(\mu=1\), the minimum value of \(w\) is determined for each \(\lambda\) and \(v\), leaving only seven possible exceptions when \(\lambda=3\) and one when \(\lambda=5\).
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 5648032
zbMATH Keywords: path design
zbMATH Keywords: embedding
zbMATH Keywords: block design
MaRDI profile type: Publication
full work available at URL: j.disc.2008.07.014
OpenAlex ID: W2058307640
cites work: Q4873725
cites work: Embedding balanced \(P_{3}\)-designs into (balanced) \(P_{4}\)-designs
cites work: Embedding path designs into kite systems
cites work: Minimum embedding of P3-designs into (K4?e)-designs
cites work: Q4842726
cites work: On complementary decompositions of the complete graph
cites work: Balanced incomplete block designs and related designs
cites work: Embeddings of \(P_{3}\)-designs into bowtie and almost bowtie systems
cites work: Embedding Steiner triple systems in hexagon triple systems
cites work: Minimum embedding of balanced \(P_{4}\)-designs into 5-cycle systems.
cites work: Embedding Steiner triple systems into Steiner systems \(S(2,4,v)\).
cites work: Minimum embedding of \(P_{3}\)-designs into \(\mathrm{TS}(v,\lambda )\)
cites work: Embedding handcuffed designs with block size 2 or 3 in 4-cycle systems
cites work: Embedding path designs in 4-cycle systems
cites work: Embedding handcuffed designs in \(D\)-designs, where \(D\) is the triangle with attached edge
cites work: Decomposition of a complete multigraph into simple paths: nonbalanced handcuffed designs
DOI: 10.1016/J.DISC.2008.07.014
description: scientific article; zbMATH DE number 5648032