P. T. de Lima

An Erd\H{o}s-P\'osa theorem for induced packings of even cycles

We show that for every graph $G$ and every positive integer $k$, $G$ contains either $k$ vertex-disjoint even cycles with no edges between distinct cycles, or a set of $O(k^2\log k)$ vertices whose closed neighborhood meets every even cycle of $G$. Moreover, we give a polynomial-time algorithm that outputs one of the t...

Odd Cycle Transversal on $H$-free graphs

\textsc{Odd Cycle Transversal} is a classic $\mathsf{NP}$-hard graph optimization problem asking for a minimum-weight set of vertices whose deletion makes the input graph bipartite, or equivalently, a maximum-weight induced bipartite subgraph. We show that \textsc{Odd Cycle Transversal} is quasi-polynomial-time solvabl...

Upper Clique Transversal on Interval Graphs and Beyond