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math.CO2024
Seymour's second neighbourhood conjecture: random graphs and reductions
Alberto Espuny Díaz, António Girão, Bertille Granet +1
A longstanding conjecture of Seymour states that in every oriented graph there is a vertex whose second outneighbourhood is at least as large as its outneighbourhood. In this short…
math.CO2024
Reconstruction of shredded random matrices
Paul Balister, Gal Kronenberg, Alex Scott +1
A matrix is given in ``shredded'' form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matr…