Opuscula Math. 39, no. 5 (2019), 623-643
https://doi.org/10.7494/OpMath.2019.39.5.623

Opuscula Mathematica

# On 1-rotational decompositions of complete graphs into tripartite graphs

Ryan C. Bunge

Abstract. Consider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let $$G$$ be a tripartite graph with $$n$$ edges, one of which is a pendent edge. This paper introduces a labeling on such a graph $$G$$ used to achieve 1-rotational $$G$$-decompositions of $$K_{2nt}$$ for any positive integer $$t$$. It is also shown that if $$G$$ with a pendent edge is the result of adding an edge to a path on $$n$$ vertices, then $$G$$ admits such a labeling.

Keywords: graph decomposition, 1-rotational, vertex labeling.

Mathematics Subject Classification: 05C78, 05C51.

Full text (pdf)

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• Communicated by Dalibor Fronček.
• Received: 2019-01-08.
• Revised: 2019-06-06.
• Accepted: 2019-06-18.
• Published online: 2019-09-05.

Cite this article as:
Ryan C. Bunge, On 1-rotational decompositions of complete graphs into tripartite graphs, Opuscula Math. 39, no. 5 (2019), 623-643, https://doi.org/10.7494/OpMath.2019.39.5.623

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