Every 3-colorable graph "G" that contains a triangle (that is, has the complete graph "K"3 as a subgraph) is homomorphically equivalent to "K"3. This is because, on one hand, a 3-coloring of "G" is the same as a homomorphism "G" → "K"3, as explained below. On the other hand, every subgraph of "G" trivially admits a homomorphism into "G", implying "K"3 → "G". This also means that "K"3 is the core of any such graph "G". Similarly, every bipartite graph that has at least one edge is equivalent to "K"2.