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math.CO2024
An improved bound on Seymour's second neighborhood conjecture
Hao Huang, Fei Peng
Seymour's celebrated second neighborhood conjecture, now more than thirty years old, states that in every oriented digraph, there is a vertex such that the size of its second o…
math.CO2024
A variable version of the quasi-kernel conjecture
Jiangdong Ai, Xiangzhou Liu, Fei Peng
A quasi-kernel of a digraph is an independent set such that every vertex can reach in at most two steps. A 48-year conjecture made by P.L. ErdÅs and Székely, denoted…