On z-cycle factorizations with two associate classes where z is 2a and a is even

Joshua Lambert, Michael Tiemeyer

Abstract


Let K = K(a, p; λ1, λ2) be the multigraph with: the number of parts equal to p; the number of vertices in each part equal to a; the number of edges joining any two vertices of the same part equal to λ1; and the number of edges joining any two vertices of different parts equal to λ2. The existence of C4-factorizations of K has been settled when a is even; when a ≡ 1 (mod 4) with one exception; and for very few cases when a ≡ 3 (mod 4). The existence of Cz-factorizations of K has been settled when a ≡ 1 (mod z) and λ1 is even, and when a ≡ 0 (mod z). In this paper, we give a construction for Cz-factorizations of K for z = 2a when a is even.


Keywords


cycles, factorization, associate classes

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DOI: http://dx.doi.org/10.5614/ejgta.2023.11.2.9

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