Is it true that, for every bipartite graph G, there exists some alpha∈ [1,2) and c>0 such that ex(n;G)sim cn^alpha? Must alpha be rational?

Erdős Problem #713 — Is it true that, for every bipartite graph $G$ , there exists some $\alpha\in [1,2)$ and $c>0$ such that $\mathrm{ex}(n;G)\sim cn^\alpha?$ Must $\alpha$ be rational?

About 56 years old · traced to 1970

Is it true that, for every bipartite graph $G$ , there exists some $\alpha\in [1,2)$ and $c>0$ such that $\mathrm{ex}(n;G)\sim cn^\alpha?$ Must $\alpha$ be rational?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

graph-theory turan-number

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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