arXiv subjects
Publications and source records attributed to Veronica Phan.
Blow-up in graph theory is a procedure in which each vertex is replaced by copies of itself, and two copies are adjacent if and only if the original vertices are adjacent. In this paper, we extend the concept of graph blow-up to a more general combinatorial context and discuss its potential applications.
In 2018, Alexander A. Razborov proved that the edge density of Fon-der-Flaass $(3,4)$-graph is $\geq\frac{7}{16}(1-o(1))$, using flag algebras. In this paper, we give an elementary proof of this result.
In this paper, we will use the entropy approach to derive a necessary and sufficient condition for the existence of an element that belongs to at least half of the sets in a finite family of sets.
A perfect graph is a graph which every induced subgraph has clique number equal to chromatic number. In this paper, I will introduce a new family of graphs, the quasiperfect graphs which generalizes the perfect graphs.
A graph is weakly perfect if its clique number and chromatic number are equal. We show that the enhanced power graph of a finite group $G$ is weakly perfect: its clique number and chromatic number are equal to the maximum order of an element of $G$. The proof requires a combinatorial lemma. We give some remarks about related graphs.