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 Apr 16 comment Proving corollary to Euler's formula by induction Ah, ok; perfect! Thanks for the clear explanation! Apr 16 comment Proving corollary to Euler's formula by induction Ah, ok. So if the walk is not closed then I need to count each edge twice, right? But yes, once this information is clear I should be able to convince myself of that. Apr 16 accepted Proving corollary to Euler's formula by induction Apr 16 revised Proving corollary to Euler's formula by induction added 165 characters in body Apr 16 revised Proving corollary to Euler's formula by induction Added LaTeX Apr 16 asked Proving corollary to Euler's formula by induction Apr 16 comment Prove that if graph $G$ is a 3-connected planar graph then its dual must be simple. Since a cycle must return to its starting vertex, a cycle beginning in $G_1$ must end in $G_1$ (it may or may not cross into $G_2$). In other words, the cycle must cross the bridges between $G_1$ and $G_2$ never or an even number of times. So that means such a cycle can only occupy two of the three available edges or none at all. Supposing the first case, if we removed the 2-occupied edges as you suggest, aren't we going to get a self-loop in the dual going across the remaining edge, which is not a simple graph? Apr 16 asked Prove that if graph $G$ is a 3-connected planar graph then its dual must be simple. Apr 7 accepted Number of storms in a rainy season Apr 7 comment Number of storms in a rainy season Yea, I didn't think the expectation looked quite right either Apr 7 asked Number of storms in a rainy season Apr 7 accepted Expectation of a parallel system Apr 7 accepted Conditioning on a random variable Apr 6 comment Planar complete tripartite graphs Let me rephrase that last part. We need not concern ourselves with a $K_5$ because a $K_5$ cannot exist in an $n$-partite graph for $n\leq 4$ by definition. It can exist in a 5-partite graph or above. Apr 6 comment Planar complete tripartite graphs Because in the case of $r\geq 3$ and $s+t \geq 3$ there exists a $K_{3,3}$. We need not be concerned with a $K_5$ because by the definition of $n$-partedness a $K_5$ shouldn't exist, correct? Apr 6 asked Planar complete tripartite graphs Apr 1 revised number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies added 12 characters in body Apr 1 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies Ah yes, I wrote the answer assuming connectedness Mar 31 answered number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies Mar 31 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies Turns out that the question was not worded correctly, I'll answer the question below how the professor intended it to be interpreted, but for all intents and purposes, you deserve the credit for helping me arrive at the conclusion and attempting to answer what was essentially a poorly worded question.