Paper
Ore's Theorem for rainbow Hamiltonian-connected graphs
Authors
Yupei Li, Ruth Luo
Abstract
Let be a collection of graphs on a common vertex set . For a graph with vertices in , we say that contains a rainbow if there is an injection such that for every edge , we have .
In this paper, we show that if is a collection of graphs on vertices such that for every , whenever , then either contains rainbow Hamiltonian paths between every pair of vertices, or contains a rainbow Hamiltonian cycle. Moreover, we prove a stronger version in which we may also embed prescribed rainbow linear forests into the Hamiltonian paths.