We give an optimal degree condition for a tripartite graph to have a spanning subgraph consisting of complete graphs of order \(3\). This result is used to give an upper bound of \(2\Delta\) for the strong chromatic number of \(n\) vertex graphs with \(\Delta \geq n/6\).
Citation
Anders Johansson, Robert Johansson, Klas Markstrom. Factors of \(r\)-partite Graphs and Bounds for the Strong Chromatic Number[J], Ars Combinatoria, Volume 095. 277-287. .