An ordered graph is a pair $\mathcal {G}=(G,\prec) $ where $ G $ is a graph and $\prec $ is
a total ordering of its vertices. The ordered Ramsey number $\overline {R}(\mathcal {G}) $ is …

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles,
and a Gallai $ k $-coloring is a Gallai coloring that uses $ k $ colors. Given an integer …

For graphs G and H, let G⟶ k H signify that any k-edge coloring of G contains a
monochromatic H as a subgraph. Let G (K 2 (N), p) be random graph spaces with edge …

For a graph H and an integer k≥ 1, the k-color Ramsey number Rk (H) is the least integer N
such that every k-coloring of the edges of the complete graph KN contains a monochromatic …

For a graph H and an integer k≥ 1, the k-color Ramsey number R k (H) is the least integer N
such that every k-coloring of the edges of the complete graph KN contains a monochromatic …

This dissertation explores two separate topics on graphs. We first study a far-reaching
generalization of the Four Color Theorem. Given a graph G, we use chi (G) to denote the …

Extremal combinatorics is one of the central branches of discrete mathematics and has
experienced an impressive growth during the last few decades. It deals with the problem of …

There is a vast amount of literature on Ramsey-type problems starting in 1930 with the
original paper of Ramsey [Ram]. Graham, Rothschild and Spencer in their book, Ramsey …

Let ex (n, C_ ≤ m) ex (n, C≤ m) denote the maximum size of a graph of order n and girth at
least m+ 1 m+ 1, and EX (n, C_ ≤ m) EX (n, C≤ m) be the set of all graphs of girth at least …

David E. Narváez Introduction Coloring Approaches Future Work Theorems about Odd Cycles
Theorems About Even Cycles C3, C5 Refer Page 1 C5-Freek-ColoringsofCompleteGraphs …