Degree sequence conditions for a graph to be disjoint path coverable

A graph G is many-to-many t-disjoint path coverable if there exist t-disjoint paths between any two disjoint vertex subsets X = {x1 , x2 , ... , xt} and Y = {y1 , y2 , ... , yt} of G such that the union of these paths covers every vertex of G. In the paper, we first provide two degree sequence sufficient conditions for a graph to be many-to-many t- disjoint path coverable. We also obtain degree sequence sufficient conditions for a graph to be one-to-many disjoint path coverable and one-to-one disjoint path coverable, which are variants of many-to-many disjoint path coverable graphs. We close the paper with analogous results for bipartite graphs.(c) 2023 Elsevier B.V. All rights reserved.