3 papers
math.CO2025
Face covers and rooted minors in bounded genus graphs
Samuel Fiorini, Stefan Kober, Michał T. Seweryn +2
A {\em rooted graph} is a graph together with a designated vertex subset, called the {\em roots}. In this paper, we consider rooted graphs embedded in a fixed surface. A collection…
math.CO2022
Reconstruction and Edge Reconstruction of Triangle-free Graphs
Alexander Clifton, Xiaonan Liu, Reem Mahmoud +1
The Reconstruction Conjecture due to Kelly and Ulam states that every graph with at least 3 vertices is uniquely determined by its multiset of subgraphs . Let $…
math.CO2021
Planar Turán Numbers of Cycles: A Counterexample
Daniel W. Cranston, Bernard Lidický, Xiaonan Liu +1
The planar Turan number is the largest number of edges in an -vertex planar graph with no -cycle. For , upper…