#### Title

Graph packing with constraints on edges

4-2016

Honors Thesis

#### Degree Name

Bachelors of Science (BS)

Mathematics

Gexin Yu

#### Committee Members

Catherine Forestell

Junping Shi

#### Abstract

A graph consists of a set of vertices (nodes) and a set of edges (line connecting vertices). Two graphs pack when they have the same number of vertices and we can put them in the same vertex set without overlapping edges. Studies such as Sauer and Spencer, Bollobas and Eldridge, Kostochka and Yu, have shown sufficient conditions, specifically relations between number of edges in the two graphs, for two graphs to pack, but only a few addressed packing with constraints. Kostochka and Yu proved that if $e_1e_2 < (1 - \eps)n^2$, then $G_1$ and $G_2$ pack with exceptions. We extend this finding by using the language of list packing introduced by Gyori, Kostochka, McConvey, and Yager, and we show that the triple $(G_1, G_2, G_3)$ with $e_1e_2 + \frac{n-1}{2}\cdot e_3 < (2 - \eps)\binom{n}{2}$ pack with well-defined exceptions.