Rainbow \(H\)-factors (Q815207)

Summary: An \(H\)-factor of a graph \(G\) is a spanning subgraph of \(G\) whose connected components are isomorphic to \(H\). Given a properly edge-colored graph \(G\), a rainbow \(H\)-subgraph of \(G\) is an \(H\)-subgraph of \(G\) whose edges have distinct colors. A rainbow \(H\)-factor is an \(H\)-factor whose components are rainbow \(H\)-subgraphs. The following result is proved. If \(H\) is any fixed graph with \(h\) vertices then every properly edge-colored graph with \(hn\) vertices and minimum degree \((1-1/\chi(H))hn+o(n)\) has a rainbow \(H\)-factor.