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Results tagged with graph-theory
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user 2757
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
14
votes
A graph on irrationals where p is adjacent to q if p^q or q^p is rational.
The answers are that $|E(G)|=2^{\aleph_0}$ and that every vertex of $G$ has degree $\aleph_0$.
Proof:
The positive real solutions to $x^y=2$ form a curve of cardinality $2^{\aleph_0}$, and at most …
- 23.8k
7
votes
Lagrange four-squares theorem: efficient algorithm with units modulo a prime?
There is also an unconditional deterministic polynomial-time algorithm to find $x,y,z,w \in \mathbf{F}_p^\times$ such that $x^2+y^2+z^2+w^2=n$, given any $n \in \mathbf{Z}$ and any prime $p \ge 7$.
F …
- 23.8k
41
votes
Accepted
Bringing Number and Graph Theory Together: A Conjecture on Prime Numbers
Theorem: Schinzel's hypothesis H implies the conjecture.
Proof: Choose distinct primes $q_S > 100|G|$ indexed by the 2-element subsets $S$ of $G$. For each $i \in G$, let $Q_i$ be the set of $q_S$ …
- 23.8k