Webb28 maj 2024 · Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few … Webb2024 FACULTY SCHOLARSHIP CELEBRATION Western Carolina University holds a proud tradition of acknowledging and celebrating our faculty’s scholarship and artistic works. 2024 marks the 31st year of this celebration and …
Gallai-Ramsey Numbers for Rainbow and Monochromatic Paths
Webb1 nov. 2024 · In this paper, we determine either the exact values or some bounds for the Gallai-Ramsey numbers gr k (P 5: H) (k ≥ 3) where H is either a fan or a wheel graph. … Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on 5 vertices. Visa mer For k \ge 3 and n \ge 6, we have Given nonnegative integers k, n, r, s, t with k \ge 1, n \ge 6 and r + s + t = k, define the number to be the minimum integer N such that every k-coloring of … Visa mer Let G be a k-coloring of a complete graph of order and suppose that G contains no rainbow triangle, no monochromatic copy of W_{n} in one of the first r colors, no monochromatic copy … Visa mer Both red and blue appear in the first rcolors. In this case, we are looking for a red or blue copy of W_{n} in G. First suppose q \le 3 so by … Visa mer nis odd. Call a part H_{i} of the Gallai partition “large” if it has order at least \frac{n - 1}{2}. We consider subcases based on the desired red and blue structures. Visa mer hy vee east main st galesburg il
Ramsey and Gallai-Ramsey Number for Wheels SpringerLink
WebbOn Ramsey numbers for paths versus wheels, Discrete Math. 307 (2007) 975–982. [28] Thomason A., Wagner P., Complete graphs with no rainbow path, J. Graph Theory 3 … Webb21 okt. 2024 · For two graphs G and H, the k -colored Gallai-Ramsey number is the minimum integer n such that every k -edge-coloring of the complete graph on n vertices contains either a rainbow copy of G or a monochromatic copy of H. This concept can be considered as a generalization of the classical Ramsey number. WebbRamsey numbers of books arise naturally in the study of r(K n;K n); indeed, Ramsey’s original proof [21] of the niteness of r(K n;K n) proceeds inductively by establishing the niteness of certain book Ramsey numbers, while the Erd}os{Szekeres bound [13] and its improvements [8, 22] are also best interpreted through the language of books. molly sebastian md facs