Let G be a tripartite unicyclic graph with eight edges that either (i) contains a triangle or heptagon, or (ii) contains a pentagon and is disconnected. We prove that G decomposes the complete graph Kn whenever the necessary conditions are satisfied. We combine this result with other known results to prove that every unicyclic graph with eight edges other than C% decomposes Kn if and only if n = 0,1 (mod 16).
|Original language||English (US)|
|Number of pages||19|
|Journal||Journal of Combinatorial Mathematics and Combinatorial Computing|
|State||Published - Aug 2020|
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