Erdős Problem #921 — Longest possible odd girth at fixed chromatic number

About 57 years old · traced to 1969

For $k≥4$ , let $f_k(n)$ be the largest possible odd girth of a $k$ -chromatic graph on $n$ vertices. Is $f_k(n)$ bounded above and below by positive constants times $n^{1/(k-2)}$ ?

References

Primary source

P. Erdős, Problems and results in chromatic graph theory, in Proof Techniques in Graph Theory (Proc. Second Ann Arbor Graph Theory Conf., 1968), Academic Press (1969), 27–35.

Additional references

P. Erdős, Problems and results in chromatic graph theory, in Proof Techniques in Graph Theory (Proc. Second Ann Arbor Graph Theory Conf., 1968), Academic Press (1969), 27–35.

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