A degree sequence is H-realizable precisely when it satisfies a generalized Erdős-Gallai-type inequality that accounts for the forced edges inside each labelled (h+1)-clique.
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Degree sequences realizing labelled $h$-factors
A degree sequence is H-realizable precisely when it satisfies a generalized Erdős-Gallai-type inequality that accounts for the forced edges inside each labelled (h+1)-clique.