Vertex cloning in a graph
= Vertex cloning in a graph
Cloning a vertex replaces it by several nonadjacent vertices with identical neighbourhoods. In <homomorphism density>, conditioning on the images of all other vertices reduces cloning to the inequality $\mathbb E p^t\ge(\mathbb E p)^t$ from the <Jensen inequality>. Iterated cloning shows that positive clique homomorphism density forces any fixed complete multipartite blow-up.