“…By the proofs of Observations 1.2 and 3.3 in [14] and [6], respectively, we know that if C is a PC cycle in a colored complete graph (complete bipartite graph), then each vertex of C is contained in a PC cycle of length 3 or 4 (4 or 6). In fact, by a similar argument, we can prove that if C is a PC cycle in a colored complete multipartite graph, then each vertex of C is contained in a PC cycle of length ∈ {3, 4, 6} (see Observation 1.9 in [13] Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.…”