Extremal problems involving vertices and edges on odd cycles
Let \(G\) be a graph on \(n\) vertices and with \(\lfloor n^2/4\rfloor+1\) or more edges. The authors investigate the minimum of the number of vertices and edges of \(G\) which are on triangles and, more generally, cycles of length \(2k+1\). They also conjecture that if \(k\geq 2\) then at least \(2n^2/9-O(n)\) edges of \(G\) are on cycles of length \(2k+1\).
scientific article; zbMATH DE number 89886