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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.
Mar
31
accepted number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies
Mar
31
revised number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies
edited title
Mar
31
comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies
Ah, I just caught that now after reading my question again. Typo, my apologies. $n$ is the number of vertices, not edges
Mar
31
revised number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies
added 4 characters in body
Mar
31
comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies
correct, I understand that, but $n$ is the total number of vertices, which is still $p+q$
Mar
31
comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies
how can $pq=n$? isn't $n= p+q$?