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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Nochumson, Shayne
Auburn University
Electrical & Electronics Engineering

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Embedding partial 3-star designs Noble, Matt; Nochumson, Shayne
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): 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/jgta.2024.12.2.9

Abstract

Define a 3-star decomposition of Kn as being a collection of subgraphs, each isomorphic to K1,3, with the property that each edge of Kn appears in exactly one of the subgraphs. A partial 3-star decomposition is similarly defined except each edge appears in at most one of the subgraphs. In this work, it is shown that any partial 3-star decomposition of Kn can be embedded into a decomposition of Kn+s where s ≤ 4. Furthermore, we determine, for any maximal partial 3-star decomposition P of Kn, the minimum s ∈{1,2,3,4} such that P can be embedded into a decomposition of Kn+s.
Co-Authors Noble, Matt