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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
14
votes
2
answers
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A tree with prime vertices
Let us construct a simple (undirected) graph $T$ as follows:
$\quad$ Let the set of all primes be the vertex set of $T$. For each prime $p$, take the least prime $q>p$ such that $2(p+1)-q$ is prime ( …
7
votes
1
answer
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A permutation problem
Here I ask a question on permutations of $n$ distinct real numbers.
QUESTION: Let $a_1,a_2,\ldots,a_n\ (n>1)$ be (pairwise) distinct real numbers. Is there a permutation $b_1,\ldots,b_n$ of $a_1,\ldo …