We study the problem of online coloring co-interval graphs. In this problem, a set of intervals on the real line is presented to the online algorithm in some arbitrary order, and the algorithm must assign each interval a color that is different from the colors of all previously presented intervals not intersecting the current interval. It is known that the competitive ratio of the simple First-...

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 wit...