Decomposition of Complete Bipartite Graphs into Cycles of Distinct Even Lengths

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• 作者：Chin-Mei Fu ; Kuo-Ching Huang ; Miwako Mishima
• 刊名：Graphs and Combinatorics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：32
• 期：4
• 页码：1397-1413
• 全文大小：469 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Engineering Design
  
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：32

文摘

Let \(K_{n,n}\) be the complete bipartite graph with two parts of equal size n. In this paper, it is shown that depending on whether n is even or odd, \(K_{n,n}\) or \(K_{n,n}-I\), where I is a 1-factor of \(K_{n,n}\), can be decomposed into cycles of distinct even lengths for any integer \(n \ge 2\) with the exception of \(n = 4\).KeywordsComplete bipartite graphCycle decomposition