Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
On Sufficient Degree Conditions for a Graph to be $k$-linked
Combinatorics, Probability and Computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Extremal Functions for Shortening Sets of Paths
Combinatorics, Probability and Computing
On the connectivity of minimum and minimal counterexamples to Hadwiger's Conjecture
Journal of Combinatorial Theory Series B
The extremal function for K9 minors
Journal of Combinatorial Theory Series B
Non-zero disjoint cycles in highly connected group labelled graphs
Journal of Combinatorial Theory Series B
Minimum degree conditions for H-linked graphs
Discrete Applied Mathematics
Linkedness and ordered cycles in digraphs
Combinatorics, Probability and Computing
Linked graphs with restricted lengths
Journal of Combinatorial Theory Series B
The extremal function for 3-linked graphs
Journal of Combinatorial Theory Series B
A weaker version of Lovász' path removal conjecture
Journal of Combinatorial Theory Series B
Balanced decomposition of a vertex-colored graph
Discrete Applied Mathematics
Linear connectivity forces large complete bipartite minors
Journal of Combinatorial Theory Series B
Linear connectivity forces large complete bipartite minors
Journal of Combinatorial Theory Series B
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Degree conditions on distance 2 vertices that imply k-ordered Hamiltonian
Discrete Applied Mathematics
A Fan-type result on k-ordered graphs
Information Processing Letters
Rank-width and tree-width of H-minor-free graphs
European Journal of Combinatorics
The disjoint paths problem: algorithm and structure
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Algorithms for finding a maximum non-k-linked graph
ESA'11 Proceedings of the 19th European conference on Algorithms
Bridges in Highly Connected Graphs
SIAM Journal on Discrete Mathematics
The Erdős-Pósa property for clique minors in highly connected graphs
Journal of Combinatorial Theory Series B
Linkage for the diamond and the path with four vertices
Journal of Graph Theory
New Ore-Type Conditions for H-Linked Graphs
Journal of Graph Theory
Connectivities for k-knitted graphs and for minimal counterexamples to Hadwiger's Conjecture
Journal of Combinatorial Theory Series B
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A graph is said to be k-linked if it has at least 2k vertices and for every sequence S1,...,Sk, t1,...,tk of distinct vertices there exist disjoint paths P1,...,Pk such that the ends of Pi are si and ti. Bollobás and Thomason showed that if a simple graph G on n vertices is 2k-connected and G has at least 11kn edges, then G is k-linked. We give a relatively simple inductive proof of the stronger statement that 8kn edges and 2k-connectivity suffice, and then with more effort improve the edge bound to 5kn.