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Decomposition of complete graphs on \(n\equiv 0,1\pmod{14}\) vertices into disconnected unicyclic tripartite graphs on seven edges

D. Banegas, L. Hawkes, A. Carlson, M. Heck, C. Higgins, Y. Hong, K. Jiang, N. Palme, X. Sundvall, J. Waadevig, B. Freyberg, D. Froncek, D. Qi

2026.1.27Journal of Combinatorial Mathematics and Combinatorial Computing

DOI: 10.61091/jcmcc129-06

Abstract

<p>Let <span class="math inline">\(G\)</span> be a disconnected tripartite unicyclic graph on seven edges with two or more connected components. We prove that <span class="math inline">\(G\)</span> decomposes the complete graph <span class="math inline">\(K_{n}\)</span> whenever <span class="math inline">\(n\equiv0,1\pmod{14}\)</span> using labeling techniques.</p>

Citation format

BANEGAS, D., et al. Decomposition of complete graphs on \(n\equiv 0,1\pmod{14}\) vertices into disconnected unicyclic tripartite graphs on seven edges. Journal of Combinatorial Mathematics and Combinatorial Computing, 2026.