Strongly Regular Graphs Page 1 Chapter 9 Strongly Regular Graphs 9.1 Strongly regular
graphs A graph (simple, undirected, and loopless) of order v is called strongly regular with …

We study two related problems concerning the number of homogeneous subsets of given
size in graphs that go back to questions of Erdős. Most notably, we improve the upper …

We study an analogue of the Ramsey multiplicity problem for additive structures, in particular
establishing the minimum number of monochromatic 3-APs in 3-colorings of $\mathbb {F} …

We study a generalization of a famous result of Goodman and establish that asymptotically
at least a $1/256$ fraction of all triangles needs to be monochromatic in any four-coloring of …

A long standing open problem in extremal graph theory is to describe all graphs that
maximize the number of induced copies of a path on four vertices. The character of the …

Tournaments are orientations of the complete graph. The directed Ramsey number R (k) is
the minimum number of vertices a tournament must have to be guaranteed to contain a …

We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-
vertex graph G can be decomposed into complete graphs C1,..., Cℓ of orders two and three …

Abstract Let R (H 1, H 2) denote the Ramsey number for the graphs H 1, H 2, and let J k be K
k− e. We present algorithms which enumerate all circulant and block-circulant Ramsey …

We study the minimum size $ f $ of a feedback vertex set in directed and undirected $ n $-
vertex graphs of given degeneracy or treewidth. In the undirected setting the bound $\frac {k …

We present a fully computer-assisted proof system for solving a particular family of problems
in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful …