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On Saturation Numbers Of Ramsey-Minimal Graphs, Hunter M. Davenport

Honors Undergraduate Theses

Dating back to the 1930's, Ramsey theory still intrigues many who study combinatorics. Roughly put, it makes the profound assertion that complete disorder is impossible. One view of this problem is in edge-colorings of complete graphs. For forbidden graphs H1,...,Hk and a graph G, we write G "arrows" (H₁,...,H_k) if every k-edge-coloring of G contains a monochromatic copy of H_i in color i for some i=1,2,...,k. If c is a (red, blue)-edge-coloring of G, we say c is a bad coloring if G contains no red K₃or blue K …