2 problems

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Erey–Hibi equality conjecture for regularity of squarefree powers of forests
Let $G$ be a forest, let $I(G)$ be its edge ideal, and for $q\geq 1$ let $I(G)^{[q]}$ be the ideal generated by squarefree monomials corresponding to matchings of size $q$ in $G$ .…
Conjectureopenedge-ideals forest-graphs squarefree-powersarXiv posted 2 days ago
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The forest characterization conjecture for the strong Erdős–Hajnal property
Forest characterization conjecture. If a tournament $H$ has an ordering of its vertices for which the backward arc digraph is a forest, then $H$ has the strong Erdős–Hajnal propert…
Conjectureopenerdos-hajnal forest-graphs tournamentsarXiv posted 2 days ago

Erey–Hibi equality conjecture for regularity of squarefree powers of forests