The Erdős-Pósa property for odd cycles in graphs of large connectivity (Q5955205)

The author proves the existence of a function \(g(k)\) such that every \(g(k)\)-connected graph is \(k\)-parity linked if the deletion of any set of less than \(4k-3\) vertices leaves a nonbipartite graph. As a consequence, the author obtains a result of Erdős-Pósa type for odd cycles in graphs of large connectivity. Moreover, the author gives six very interesting conjectures for futher studying and also some connections between these conjectures.