k-linked and k-cyclic digraphs
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Alternating paths in edge-colored complete graphs
Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Sufficient Degree Conditions for a Graph to be $k$-linked
Combinatorics, Probability and Computing
Linkedness and ordered cycles in digraphs
Combinatorics, Probability and Computing
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
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A graph is k-linked (k-edge-linked), k=1, if for each k pairs of vertices x"1,y"1,...,x"k,y"k, there exist k pairwise vertex-disjoint (respectively edge-disjoint) paths, one per pair x"i and y"i, i=1,2,...,k. Here we deal with the properly edge-colored version of the k-linked (k-edge-linked) problem in edge-colored graphs. In particular, we give conditions on colored degrees and/or number of edges, sufficient for an edge-colored multigraph to be k-linked (k-edge-linked). Some of the results obtained are the best possible. Related conjectures are proposed.