Research
Extremal Graph theory is one of the most interesting fields in modern Graph theory. It has risen in popularity over the course of the last few decades. The problems include finding the maximum number of edges or particular subgraphs when certain subgraphs are prohibited. Through my doctoral period, I have tackled various problems in the Field of Extremal Combinatorics. I worked on the classical Turán problem for graphs before branching out into “Generalized Turán problems”. The growing field of Planar Turán problems interested me the most. I briefly explored the natural generalization of Turán type problems in hypergraphs. In addition, I applied the concepts of Planar Extremal Graph Theory in determining the Wiener index of planar graphs.
Publications:
Planar Turán Number of Double Stars with E. Győri, A. Paulos, C. Xiao.
Book free 3-Uniform Hypergraphs with E. Győri, J. Nagy-György, A. Paulos, C. Xiao, O. Zamora.
The Turán Number of the Triangular Pyramid of 3-Layers with E. Győri, A. Paulos, C. Xiao, O. Zamora. Accepted in: J. Discrete Mathematics.
Planar Turán Number of the θ_6 with E. Győri, A. Paulos, C. Xiao, O. Zamora.
The Maximum Number of Paths of Length Four in a Planar Graph with E. Győri, R. R. Martin, A. Paulos, N. Salia, C. Xiao, O. Zamora. Accepted in: Discrete Mathematics. 344(5) (2021).
Planar Turán number of the 6-cycle with E. Győri, R. R. Martin, A. Paulos, C. Xiao. Accepted in: J. Discrete Mathematics.
The maximum number of induced C_5’s in a Planar Graph with E. Győri, O. Janzer, A. Paulos, N. Salia, O. Zamora. Accepted in: J. Graph Theory. 99(3) (2022), 378-398.
The Maximum Wiener Index of Maximal Planar Graphs with E. Győri, A. Paulos, N. Salia, O. Zamora. Accepted in: J. Combinatorial Optimization. 40 (2020), 1121–1135.
Determinants of Representations of Coxeter Groups with S. Spallone. Accepted in: J. Algebraic Combin. 49(3) (2019), 229-265.