Uniform coverings of 2-paths with 4-cycles
type: Item
instance of: scholarly article
title: Uniform coverings of 2-paths with 4-cycles
zbMATH Open document ID: 1330.05130
author: Midori Kobayashi
author: Keiko Kotani
author: Nobuaki Mutoh
author: Gisaku Nakamura
published in: AKCE International Journal of Graphs and Combinatorics
publication date: 2015-12-11T00:00:00Z
review text: For a graph \(G\) and a subgraph \(H\) of \(G\), a \(D(G, H, \Lambda)\) design is a multiset \(D\) of subgraphs of \(G\), each of which is isomorphic to \(H\) so that every path of length 2 lies in exactly \(\Lambda\) subgraphs in \(D\). Likewise, for a digraph \(G\) and a subgraph \(H\) of \(G\), a \(D(G, H, \Lambda)\) design is a multiset \(D\) of subgraphs of \(G\), each of which is isomorphic to \(H\) so that every directed path of length 2 lies in exactly \(\Lambda\) subgraphs in \(D\). These designs are referred to as Dudeney designs. The paper shows that for \(n \geq 2\) and \(\Lambda \geq 1\) there exists a Dudeney design for the \(2n\)-node complete bipartite graph with cycle of length 4 if and only if (i) \(n\) is even, or (ii) \(n\) is odd and \(\Lambda\) is even. It is also shown that for \(n \geq 2\) and \(\Lambda \geq 1\), there exists a Dudeney design for the \(2n\)-node complete bipartite digraph with directed cycle of length 4.
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C51
zbMATH DE Number: 6520419
zbMATH Keywords: Dudeney design
zbMATH Keywords: covering of 2-paths
zbMATH Keywords: covering with 4-cycles
reviewed by: Wai-Kai Chen
MaRDI profile type: Publication
full work available at URL: j.akcej.2015.06.011
OpenAlex ID: W2251169064
cites work: Q2960943
cites work: Covering 2-paths uniformly
cites work: Uniform coverings of 2-paths in the complete bipartite directed graph
cites work: Exact coverings of 2-paths by 4-cycles
cites work: Resolvable coverings of 2-paths by 4-cycles
DOI: 10.1016/J.AKCEJ.2015.06.011
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description: scientific article; zbMATH DE number 6520419