Frontiers of Mathematics in China >
Almost resolvable maximum packings of complete graphs with 5-cycles
Received date: 08 Nov 2013
Accepted date: 20 Aug 2014
Published date: 12 Feb 2015
Copyright
Let X be the vertex set of KnA k-cycle packing of Kn is a triple (X,C,L), where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing (X,C,L) is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP(n), is a resolvable k-cycle packing of Kn, (X,C,L), in which the number of almost parallel classes is as large as possible. Let D(n, k) denote the number of almost parallel classes in a k-RMCP(n). D(n, k) for k = 3, 4 has been decided. When n ≡ k (mod 2k) and k ≡ 1 (mod 2) or n ≡ 1 (mod 2k) and k ∈{6, 8, 10, 14}∪{m: 5≤m≤49, m ≡ 1 (mod 2)}, D(n, k) also has been decided with few possible exceptions. In this paper, we shall decide D(n, 5) for all values of n≥5.
Key words: Cycle packing; resolvable maximum cycle packing; cycle frame
Min ZHOU , Haitao CAO . Almost resolvable maximum packings of complete graphs with 5-cycles[J]. Frontiers of Mathematics in China, 2015 , 10(2) : 461 -475 . DOI: 10.1007/s11464-015-0425-7
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