All Questions
3 questions
5
votes
1
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386
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Are directed graphs with out-degree exactly 2 strongly connected with probability 1?
Consider a directed graph with out-degree exactly two with $n$ vertices $v_1, v_2 \cdots v_n$ that is constructed as follows: For each vertex $v_i$, one chooses uniformly at random two (not ...
6
votes
0
answers
116
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The properties of almost all directed graphs
A mathematician on the forum previously requested a reference on human brains modelled as directed graphs. This makes sense as neurons are mostly unidirectional and I have been thinking about similar ...
0
votes
1
answer
166
views
Length of longest directed circuit in random tournament
Build a random tournament $T=(V,E)$ on $V=\{1,\ldots, n\}$ in the following fashion: for $i < j\in \{1,\ldots, n\}$ let the probability be $0.5$ whether $(i,j)\in E$ or $(j,i)\in E$ (in a ...