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Resilient forest universality in percolated dense graphs
Mostafa Mirabi
Christoph, Müyesser and Wigderson recently asked whether an approximate form of the Erdős-Sós conjecture is robust under random edge deletions. We establish a density-sensitive tra…
One-point extensions of Euclidean Ramsey sets
Mostafa Mirabi
Let be a finite Euclidean Ramsey set. We prove that adjoining any point outside the affine hull of gives another Euclidean Ramsey set, answering a conjecture of Ivan, Leade…
Structured Sunflowers
Nathanael Ackerman, Mary Leah Karker, Mostafa Mirabi
We call an infinite structure sunflowerable if whenever is isomorphic to with underlying set , consisting of finite sets of bounded s…
Rainbow Threshold Graphs
Nathanael Ackerman, Mostafa Mirabi
We define a generalization of threshold graphs which we call -rainbow threshold graphs. We show that the collection of -rainbow threshold graphs do not satisfy the - la…
Algebraic Sunflowers
Nathanael Ackerman, Mostafa Mirabi
We study sunflowers within the context of finitely generated substructures of ultrahomogeneous structures. In particular, we look at bounds on how large a set system is needed to g…
From Shelah's block-content to Hales-Jewett
Mohammad Golshani, Mostafa Mirabi, Saharon Shelah
We study the quantitative relationship between the Hales-Jewett numbers and Shelah's block-content canonization functions. Block-content canonization yields a block subspace on whi…