How can you prove that a cubic graph with a bridge cannot be 3-edge colored? I guess one could try a proof by contradiction, so we assume a 3 edge coloring is possible for such a graph. But then I am not sure in which direction to continue. I have tried to draw such graphs, and clearly, they can't be 3 edge-colored. But a more formal proof would be helpful. Or maybe a proof by contrapositive, so let say we have a cubic graph with a 3-edge coloring. How do we show this graph is bridgeless?