Year: 2025
Type: article
Abstract: Every red-blue coloring of the edges of a graph G results in a sequence G1, G2, . .., G ℓ of pairwise edge-disjoint monochromatic subgraphs Gi (1A galaxy is a graph each of whose components is a star.For a positive integer s, an s-galaxy consists of s stars.Thus, a 1-galaxy of size m is the star Sm and an m-galaxy of size m is the matching mK2.A 2-galaxy Sx + Sm-x is a galaxy consisting of the two stars Sx and Sm-x for positive integers x and m ≥ 2. The Ramsey indexes of 1-galaxies and m-galaxies are known as well as all 2-galaxies Sx + Sm-x for integers x = 1, 2 and m ≥ 3. Here, the exact values of AR(Sx + Sm-x) are determined for integers x = 3, 4 and m ≥ 6.Additional results and conjectures on Ramsey chains in 2-galaxies are also presented.
Authors: Ritabrato Chatterjee, Ping Zhang
Institution: Western Michigan University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413849681