1 research outputs found
Enomoto and Ota's conjecture holds for large graphs
In 2000, Enomoto and Ota conjectured that if a graph satisfies
, then for any set of vertices and for any positive integers with , there exists a partition of into paths
such that is an end of and for all . We
prove this conjecture when is large. Our proof uses the Regularity Lemma
along with several extremal lemmas, concluding with an absorbing argument to
retrieve misbehaving vertices