Subdivisions of a graph of maximal degree \(n+1\) in graphs of average degree \(n+\epsilon\) and large girth (Q5955200)

In the paper it is proved that for every integer \(n\geq 2\) and every \(\epsilon>0\), there is a least positive integer \(t(n,\epsilon)\) such that for every finite graph of average degree at least \(n+\epsilon\) and of girth at least \(t(n,\epsilon)\) contains a subdivision of the complete graph on \(n+2\) vertices. The values of \(t(2,\epsilon)\) are determined for every \(\epsilon>0\).