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On the difference between clique partition and clique covering numbers
For a graph \(G\), let \(\operatorname{cp}(G)\) and \(\operatorname{cc}(G)\) be the minimum numbers of cliques in an edge partition and a clique cover of \(G\), respectively. Set $σ_n = \max_{\lvert V(G)\rvert=n} \bigl(\operatorname{cp}(G)-\operatorname{cc}(G)\bigr), d_n=\left\lfloor\frac{n^2}{4
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