4 problems

Let $\mathcal{S}$ be the class of forests in which every connected component is a tree with at most three leaves; its members are called tripods. A hereditary class is finitely-def…

An induced packing of cycles is a collection of cycles such that no edge joins distinct cycles. A graph class has no induced packing of $k$ cycles if no graph in the class contains…

Polynomial-time independent-set conjecture. $\textsc{Maximum Independent Set}$ is solvable in polynomial time in $\mathcal{O}_k$-free graphs.

Let $(\beta,h,\gamma)$ be parameters of the independent set problem, and let an MP-structure consist of a hierarchy $(\zeta,\mathcal V_{\boldsymbol m})$ with $K$ levels. For such a…