Heather Jordon

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In this paper, we settle Alspach’s problem in the case of Hamilton cycles and 5cycles; that is, we show that for all odd integers n ≥ 5 and all nonnegative integers h and t with hn + 5t = n(n − 1)/2, the complete graph Kn decomposes into h Hamilton cycles and t 5-cycles and for all even integers n ≥ 6 and all nonnegative integers h and t with hn+5t =(More)
For a signed graph G and function f : V ðGÞ ! Z , a signed f -factor of G is a spanning subgraph F such that sdegF ðvÞ 1⁄4 f ðvÞ for every vertex v of G, where sdegðvÞ is the number of positive edges incident with v less the number of negative edges incident with v, with loops counting twice in either case. For a given vertex-function f , we provide(More)
In this paper, we prove that directed cyclic hamiltonian cycle systems of the complete symmetric digraph, K∗ n, exist if and only if n ≡ 2 (mod 4) and n 6= 2p with p prime and α ≥ 1. We also show that directed cyclic hamiltonian cycle systems of the complete symmetric digraph minus a set of n/2 vertex-independent digons, (Kn− I)∗, exist if and only if n ≡ 0(More)
A k-extended Skolem-type 5-tuple difference set of order t is a set of t 5-tuples {(di,1, di,2, di,3, di,4, di,5) | i = 1, 2, . . . , t} such that di,1+di,2+di,3+di,4+di,5 = 0 for 1 ≤ i ≤ t and {|di,j| | 1 ≤ i ≤ t, 1 ≤ j ≤ 5} = {1, 2, . . . , 5t+1}\{k}. In this talk, we will give necessary and sufficient conditions on t and k for the existence of a(More)
Let G of order n be the vertex-disjoint union of an even and an odd cycle. It is known that there exists a G-decomposition of K v for all v ≡ 1 (mod 2n). We use an extension of the Bose construction for Steiner triple systems and a recent result on the Oberwolfach Problem for 2-regular graphs with two components to show that there exists a G-decomposition(More)