Combinatorial approximation of maximum $k$-vertex cover in bipartite graphs within ratio~0.7

We propose a $\mathit{\text{purely}}\mathit{\text{combinatorial}}\mathit{\text{algorithm}}$ for \mkvc{} in bipartite graphs, achieving approximation ratio~0.7. The only combinatorial algorithms currently known until now for this problem are the natural greedy algorithm, that achieves ratio 0.632, and an easy~$2\mathrm{/}3$-approximation algorithm presented in \cite{DBLP:journals/corr/BonnetEPS14}.