2021/09/06 by Yaser Rowshan, Rowshan, Yaser
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO
paper · pdf · doi:10.48550/arxiv.2109.02257
A fundamental flaw has been discovered in the proof of the main theorem (Theorem 1.2), and the theorem is not valid in general
openalex publication_date 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv created 2026/08/03 · arxiv updated 2026/08/04
Assume that Kj× n be a complete, multipartite graph consisting of j partite sets and n vertices in each partite set. For given graphs G1 and G2, the multipartite Ramsey number (M-R-number) mj(G1, G2) is the smallest integer t such that any subgraph G of the Kj× t, either G contains a copy of G1 or its complement relative to Kj× t contains a copy of G2. C. J. Jayawardene, E. T. Baskoro et al. (2016) gave the size of M-R-numbe mj(nK2, C7) for j ≥ 2 and n≤ 6. Y. Rowshan et al. (2021) gave the size of M-R-number mj(nK2, C7) for j = 2,3, 4 and n≥ 2. In this article we compute the size of M-R-number mj(nK2,C7), for each j≥ 5 and n≥ 2.