5 problems

For each $\ell\geq 3$, let $C_\ell$ be the cycle of length $\ell$. A hole is an induced cycle of length at least $4$, and a graph is $C_4$-free if it contains no $C_4$. Let…

Let $C_4$ denote the cycle of length $4$. A hole is an induced cycle of length at least $4$, and a graph is $C_4$-free if it contains no cycle of length $4$. For a graph $G$ and…

For a graph family with the Erdős–Pósa property, let $k$ be the packing parameter and let the objects' length be measured by the relevant notion for that family. Long Erdős–Pósa co…

Condensed-wall conjecture. $H$ has the edge-Erdős–Pósa property.

Multiple-constraint Erdős–Pósa conjecture. The set of all $\bigoplus_{i=1}^t\Gamma_i$-labeled graphs has the half-integral Erdős–Pósa property for $(\Gamma_1,\dots,\Gamma_t)$-non-z…