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Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo
Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo
Honors Undergraduate Theses
The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For a graph H, the k-color Ramsey number r(H; k) of H is the smallest integer n such that every k-edge-coloring of Kn contains a monochromatic copy of H. Despite active research for decades, very little is known about Ramsey numbers of graphs. This is especially true for r(H; k) when k is at least 3, also known as the multicolor Ramsey number of …
Gallai-Ramsey Numbers For C7 With Multiple Colors, Dylan Bruce
Gallai-Ramsey Numbers For C7 With Multiple Colors, Dylan Bruce
Honors Undergraduate Theses
The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. One view of this problem is in edge-colorings of complete graphs. For any graphs G, H1, ..., Hk, we write G → (H1, ..., Hk), or G → (H)k when H1 = ··· = Hk = H, if every k-edge-coloring of G contains a monochromatic Hi in color i for some i ∈ …