2 problems

Let $C_n$ be a cycle of order $n=2k+x$, with $k\geq2$ and $1\leq x\leq2k-1$. The parameter $\lambda^k(C_n)$ is the largest number of labels in a labeling of the vertices that admit…

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…