Research
Papers:
(1) The Nash-Williams Orientation Theorem for graphs with countably many ends, with Max Pitz and Marcel Koloschin, October 2023, arxiv.org/abs/2310.03601.
In this paper we showed that the orientation conjecture of Nash-Williams (that 2k-edge-connectivity implies the existence of a k-arc-connected orientation) is true for locally finite graphs with countably many ends.
(2) Towards Nash-Williams Orientation Conjecture for Infinite Graphs, June 2023, arxiv.org/abs/2306.10631.
In this paper I showed that edge-connectivity of 4k is sufficient for a 1-ended locally finite graph to admit a k-arc-connected orientation.
(3) Analysis of the Lifting Graph, December 2022 , arxiv.org/pdf/2212.03347.pdf.
This paper is based on the central chapter of my PhD thesis. In it I provide a comprehensive study of the lifting graph, which is an auxiliary graph used in edge-connectivity proofs. Lifting was previously studied by Lov\'asz, Mader, Frank, Jordan, Ok, Richter, and Thomassen.
During 2023: With Bertrand Guenin, we worked on problems related to Woodall's conjecture on disjoint dijoins. We specifically tried introducing a model that aims to generalize the fractional packings of trees and of dijoins. With Bruce Richter, we continued working on Thomassen's weak linkage conjecture and tried to improve the results from my PhD thesis. With Max Pitz, we made progress towards the orientation conjecture of Nash-Williams for infinite graphs.
From October to December 2023 I also did Operations Research at WANOPT.
January 2018 - September 2022:
In my PhD thesis, under the suprivsion of Bruce Richter, I improved Thomassen's results regarding both, the orientation conjecture of Nash-Williams, and Thomassen's weak linkage conjecture, in infinite graphs.
uwspace.uwaterloo.ca/handle/10012/18790
2015-2017:
In my masters thesis at Waterloo I proved that graphs that are two edges far away from planar are still 5-choosable. This work extends results of Carsten Thomassen, and of Luke Postle . Done under the guidance of Bruce Richter.
https://uwspace.uwaterloo.ca/handle/10012/12798
2012-2014:
I did my first masters thesis, at Cairo University, under the supervision of Wafik Boulos Lotfallah. It was in the subjects of Finite Model Theory and Descriptive Complexity. The finite models I worked with were graphs, and I used games on graphs to study definability and the correspondence between the computational complexity and the complexity of expression (level or order of logic used to describe a property of graphs).