A Strengthening of Erdős-Gallai Theorem and Proof of Woodall's Conjecture

Binlong Li, Bo Ning

For a 2-connected graph $G$ on $n$ vertices and two vertices $x,y\in V(G)$, we prove that there is an $(x,y)$-path of length at least $k$ if there are at least $\frac{n-1}{2}$ vert…