Erdős–Pósa property of obstructions to interval graphs

A class of graphs ℱ ${\rm{ {\mathcal F} }}$ admits the Erdős–Pósa property if for any graph G $G$ , either has k $k$ vertex-disjoint “copies” in or there is a set S ⊆ V ( ) $S\subseteq V(G)$ f $f(k)$ vertices that intersects all copies . For ${\mathscr{G}}$ it natural to ask whether family obstructions property. In this paper, we prove interval graphs—namely, chordless cycles and asteroidal witnesses (AWs)—admits turn, yields an algorithm decide given AWs cycles, exists O 2 log ${\mathscr{O}}({k}^{2}\mathrm{log}k)$ hits cycles.