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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Joshua Lambert
Department of Mathematical Sciences, Georgia Southern University, USA
Electrical & Electronics Engineering

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On z-cycle factorizations with two associate classes where z is 2a and a is even Joshua Lambert; Michael Tiemeyer
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.9

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.
Co-Authors Michael Tiemeyer