Enomoto and Ota's conjecture holds for large graphs

In 2000, Enomoto and Ota conjectured that if a graph $G$ satisfies ${\sigma }_2(G)\ge n+k-1$, then for any set of $k$ vertices $v_{1}, \dots, v_{k}$andforanypositiveintegers$n_{1}, \dots, n_{k}$with$\sum n_{i} = |G|$,thereexistsapartitionof$V(G)$into$k$paths$P_{1}, \dots, P_{k}$suchthat$v_{i}$isanendof$P_{i}$and$|P_{i}| = n_{i}$forall$i$. We prove this conjecture when $\mathrm{\mid }G\mathrm{\mid }$ is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices.