Is there a connected nonplanar graph with 7 vertices which is 3-chromatic (it is the minimal number needed for coloring) and has no Euler cycle?

Is there a connected nonplanar graph with 7 vertices which is 3-chromatic (it is the minimal number needed for coloring) and has no Euler cycle? Is there such a graph without both an Euler cycle and a Hamiltonian Cycle? Provide an explanation and drawing (with edge intersections if needed in both cases is the graph (or graphs) exist.