Gallai‐Ramsey number for K4. Issue 2 (8th November 2019)

• Record Type: Journal Article
• Authors: Liu, Henry; Magnant, Colton; Saito, Akira; Schiermeyer, Ingo; Shi, Yongtang
• Is Part Of: Journal of graph theory. Volume 94:Issue 2(2020)
• Page Start: 192
• Page End: 205
• Publication Date: 2019-11-08
• Subjects: Gallai‐coloring -- rainbow triangle -- Ramsey; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22514
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: Given a graph H, the k ‐colored Gallai‐Ramsey number g r k ( K 3 ⁢ : H ) is defined to be the minimum integer n such that every k ‐coloring (using all k colors) of the complete graph on n vertices contains either a rainbow triangle or a monochromatic copy of H . Recently, Fox et al [J. Combin. Theory Ser. B, 111 (2015), pp. 75–125] conjectured the value of the Gallai‐Ramsey numbers for complete graphs. We verify this conjecture for the first open case, where H = K 4 .