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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
732 views

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 ( …
Zhi-Wei Sun's user avatar
  • 15.6k
7 votes
1 answer
504 views

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 …
Zhi-Wei Sun's user avatar
  • 15.6k