For edge clique partition and cover parameterized above the independence number, the paper gives an FPT algorithm for the partition variant, an NP-completeness dichotomy for the cover variant, and FPT algorithms on bounded-clique, degenerate, and minor-free graphs.
Boole, Of Propositions Numerically Definite , Watts, London, 1952
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Edge Clique Partition and Cover Beyond Independence
For edge clique partition and cover parameterized above the independence number, the paper gives an FPT algorithm for the partition variant, an NP-completeness dichotomy for the cover variant, and FPT algorithms on bounded-clique, degenerate, and minor-free graphs.