A Short Derivation for Turán Numbers of Paths

Source abstract

This paper gives a short derivation for a result by Faudree and Schelp that the Turán number $\operatorname{ex}(n;P_{k+1})$ of a path of $k+1$ vertices is equal to $q \binom{k}{2} + \binom{r}{2}$, where $n = qk+r$ and $0 \leq r \lt k$, with the set $\operatorname{EX}(n;P_{k+1})$ of extremal graphs determined.