1) V1 For every fixed k≥3, is there a constant c_k>0 such that every sufficiently large N admits a C_{2k}-free simple graph with at least c_k N^(1+1/k) edges?
open, filed Tue Aug 25 2026 06:42:32 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The graph/cycle encoding is direct and finite. Empty graphs exclude cycles and the complete graph on six vertices kernel-checks a genuine wrapped six-cycle; an independent encoding is definitionally equal; nine content-free bridges fail. Whole routes checked random deletion, algebraic high-girth/Ramanujan constructions, generalized polygons, norm/polarity graphs, and definition degeneracies.
Scope. Erdős problem 572's exact all-k lower-bound conjecture. Graphs are finite simple edge sets; a cycle uses 2k distinct vertices with every consecutive edge including wraparound; the extremal number maximizes edges among C_{2k}-free graphs.