Note on Enomoto and Ota's Conjecture for Short Paths in Large Graphs.

With sufficient minimum degree sum, Enomoto and Ota conjectured that for any selected set of vertices, there exists a spanning collection of disjoint paths, each starting at one of the selected vertices and each having a prescribed length. Using the Regularity Lemma, we prove that this claim holds without the spanning assumption if the vertex set of the host graph is sufficiently large. [ABSTRACT FROM AUTHOR]