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.

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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.
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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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