Embedding finite graphs into graphs colored with infinitely many colors (Q1182823)

The following theorem is proved: For any cardinal number \(\tau\) and for any finite graph \(H\), there exists a graph \(G\) such that, for any coloring of the pairs of vertices of \(G\) with \(\tau\) colors, there exists a copy of \(H\), as an induced subgraph of \(G\), so that both the edges of the copy and the edges of the complement of the copy are monochromatic.