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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Luke Branson
University of Minnesota Duluth
Electrical & Electronics Engineering

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On decompositions of complete graphs into unicyclic disconnected bipartite graphs on nine edges Alan Bonhert; Luke Branson; Patrick Joseph Otto
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

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Abstract

We use Rosa-type labelings to decompose complete graphs into unicyclic, disconnected, bipartite graphs on nine edges – namely, those featuring cyclic component C4, C6, or C8. For any such graph H, we prove there exists an H-design of K18k + 1 and K18k for all positive integers k.
Co-Authors Alan Bonhert Patrick Joseph Otto