  Structural parameters of graph (such as degeneracy and arboricity) had rarely
been considered when designing algorithms for $\textit{(edge) clique cover}$
problems. Taking degeneracy of graph into account, we present a greedy
framework and two fixed-parameter tractable algorithms for $\textit{clique
cover}$ problems. We introduce a set theoretic concept and demonstrate its use
in the computations of different objectives of $\textit{clique cover}$.
Furthermore, we show efficacy of our algorithms in practice.
