… We will also call Hamilton cycles arrangements since they are an arrangement of the vertices
of K,, The … Such a family of cycles will be calied an exact covering of the 2-paths of Y, by k-…

… (A Hamilton cycle double cover of a graph is a collection of Hamilton cycles such that every
edge of the … The complete graphs KV1 and KV2 have Hamilton cycle double covers.) Put …

… i mg be a set of m Hamilton cycles in Kn. If A satisfies conditions (1) and (2), A is called an
antipodal Hamilton cycle double cover of Kn: (1) A is a Hamilton cycle double cover of Kn, that …

… has a Hamilton cyde is called the Hamilton cycle problem. … precise, G is a 2-edge-connected
simple graph with no cycle … admits a decomposition 9 into n/2 paths. Since each vertex of G …

… The problem is equivalent to asking for a set of Hamilton cycles in the … of the cycles. The
length of a path is the number of edges in the path. A Cðn, k, kÞ design is a multiset of k-cycles in …

… The problem of finding a set of (n - l)(n - 2)/2 Hamilton cycles in K, so that every path of length
two (2-path) occurs on exactly one Hamilton cycle was first looked at by Judson in 1899 [9]. …

… Using this notation we now construct a specific double Hamilton cycle cover of K,,, = (V,, E,),
where V, = (fi, f2, . . . . f,}, m is even, and m > 4, which will be used in Section 4. Let C be the …

… we identify the exact Dirac threshold for Hamilton 2-cycles in 4-… H, we can cover almost all
vertices of H by a long 2-cycle C of … this section we only consider 2-paths and 2-cycles, so we …

… For constant p, we will give an exact formula. … be decomposed into ⌈ n / 2 ⌉ paths. The
result of Lovász mentioned … packing Hamilton cycles in G n , p which together cover essentially …

… of complete graphs into Hamilton cycles or Hamilton paths was … be decomposed into fewer
than ⌊ n 2 ⌋ paths and cycles. … ∗ , and at each stage we cover exceptional vertices of highest …