Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Biro, Csaba

Committee Co-Chair (if applicable)

Kezdy, Andre

Committee Member

Kezdy, Andre

Committee Member

Riedel, Thomas

Committee Member

Seif, Steven

Committee Member

Bai, Lihui

Author's Keywords

Graph theory; partially ordered sets; Ramsey theory; interval orders; semi-orders; dimension theory


In this dissertation, there are two major parts. One is the dimension results on different classes of partially ordered sets. We developed new tools and theorems to solve the bounds on interval orders using different number of lengths. We also discussed the dimension of interval orders that have a representation with interval lengths in a certain range. We further discussed the interval dimension and semi dimension for posets. In the second part, we discussed several related results on the Ramsey theory of grids, the results involve the application of Product Ramsey Theorem and Partition Ramsey Theorem