文章基本信息

标题：Uniform coverings of 2-paths with 4-cycles
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作者：Midori Kobayashi ; Midori Kobayashi ; Keiko Kotani 等
期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2015
卷号：12
期号：1
页码：70-73
DOI：10.1016/j.akcej.2015.06.011
语种：English
出版社：Elsevier
摘要：Abstract Let G be a graph [a digraph] and H be a subgraph of G . A D ( G , H , λ ) design is a multiset D of subgraphs of G each isomorphic to H so that every 2-path [directed 2-path] of G lies in exactly λ subgraphs in D . In this paper, we show that there exists a D ( K n , n , C 4 , λ ) design if and only if (i) n is even, or (ii) n is odd and λ is even. We also show that there exists a D ( K n , n ∗ , C ⃗ 4 , λ ) design for every n and λ , where K n , n and K n , n ∗ are the complete bipartite graph and the complete bipartite digraph, respectively; C 4 and C ⃗ 4 are a 4-cycle and a directed 4-cycle, respectively.
关键词：KeywordsenDudeney designCovering of 2-pathsCovering with 4-cycles