Linked graphs with restricted lengths

A graph G is k-linked if G has at least 2k vertices, and for every sequence x1, x2, . . . , xk, y1, y2, . . . , yk of distinct vertices, G contains k vertex-disjoint paths P1, P2, . . . , Pk such that Pi joins xi and yi for i = 1, 2, . . . , k. Moreover, the above defined k-linked graph G is k-linked modulo (m1, m2, . . . , mk) if, in addition, for any ktuple (d1, d2, . . . , dk) of natural numbers, the paths P1, P2, . . . , Pk can be chosen such that Pi has length di modulo mi for i = 1, 2, . . . , k. Thomassen showed that there exists a function f(m1, m2, . . . , mk) such that every f(m1, m2, . . . , mk)-connected graph is k-linked modulo (m1, m2, . . . , mk) provided all mi are odd. For even moduli, he showed in another article that there exists a natural number g(2, 2,

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: Guantao Chen, Yuan Chen, Shuhong Gao, Zhiquan Hu
• Keywords: Distinct Vertices, JCT 2008, Natural Number, Paths P1