Erdős girth conjecture

Conjecture

For every $k \geq 1$, there exists an $n$-node graph with $\Omega(n^{1+1/k})$ edges and girth at least $2k+2$.

(where girth refers to the length of the shortest cycle contained in the graph)

(unproven?)

References

1. https://people.csail.mit.edu/ghaffari/AA18/Notes/S2.pdf
2. Paul Erdős. Extremal problems in graph theory. In IN THEORY OF GRAPHS AND ITS APPLICATIONS, PROC. SYMPOS. SMOLENICE. Citeseer, 1964.
   • Erdős, P.: Extremal problems in graph theory. In: Proc. Symp. Theory of Graphs and its Applications, pp. 29–36 (1963) https://scispace.com/pdf/an-extremal-problem-in-graph-theory-1jqedkg5za.pdf
   • P. Erdös and L. Moser, “An extremal problem in graph theory,” J. Aust. Math. Soc., vol. 11, no. 1, pp. 42–47, Feb. 1970, doi: 10.1017/S1446788700005954.