Spanning H -subdivisions and perfect H -subdivision tilings in dense digraphs

Given a (di)graph upper H H H , we say that a (di)graph upper H prime H ′ H is an upper H H H -subdivision if upper H prime H ′ H is obtained from upper H H H by replacing one or more edges with internally vertex-disjoint paths. Pavez-Signé conjectured that for every epsilon greater than 0 ε > 0 ε > 0 , there exists a constant upper C 0 greater than 0 C 0 > 0 C₀> 0 such that for every graph upper H H H with h h