3. A walk around Königsberg which would cross each of the seven bridges exactly once is equivalent to an Euler path. Corollary 11.2.5 states that that there is an Euler path from v to w in G if, and only if, G is connected, v and w have odd degree, and all other vertices have even degree. Since all the vertices in the Königsberg bridge graph have odd degree (see graph below), there is no Euler path in this graph, so there is no way to walk around Königsberg and cross all seven bridges exactly once.