Jeremy Lyle

Dense graphs with small clique number

We consider the structure of Kr-free graphs with large minimum degree, and show that such graphs with minimum degree δ>(2r − 5)n/(2r − 3) are homomorphic to the join Kr − 3∨H, where H is a triangle-free graph. In particular this allows us to generalize results from triangle-free graphs and show that Kr-free graphs with such a minimum degree have chromatic number at most r +1. We also consider the minimum-degree thresholds for related properties. Copyright

On the Chromatic Number of H -Free Graphs of Large Minimum Degree

The problem of determining the chromatic number of H-free graphs has been well studied, with particular attention to Kr-free graphs with large minimum degree. Recent progress has been made for triangle-free graphs on n vertices with minimum degree larger than n/3. In this paper, we determine the family of r-colorable graphs

A Structural Approach for Independent Domination of Regular Graphs

{\mathcal{H}_r}

A note on the annihilation number and 2-domination number of a tree

, such that if

On the Independent Domination Number of Regular Graphs

{H \in \mathcal{H}_r}

The binding number of a graph and its cliques

, there exists a constant C < (r − 2)/(r − 1) such that any H-free graph G on n vertices with δ(G) > Cn has chromatic number bounded above by a function dependent only on H and C. A value of C < (r − 2)/(r − 1) is given for every