Graph minors. VI. Disjoint paths across a disc
Journal of Combinatorial Theory Series B
Construction of crossing-critical graphs
Discrete Mathematics
Graph minors. IV. Tree-width and well-quasi-ordering
Journal of Combinatorial Theory Series B
Minimal graphs with crossing number at least k
Journal of Combinatorial Theory Series B
Typical subgraphs of 3- and 4-connected graphs
Journal of Combinatorial Theory Series B
SIAM Journal on Discrete Mathematics
Crossing-number critical graphs have bounded path-width
Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
On the decay of crossing numbers
Journal of Combinatorial Theory Series B
Crossing numbers of sequences of graphs II: Planar tiles
Journal of Graph Theory
Note: Crossing-critical graphs with large maximum degree
Journal of Combinatorial Theory Series B
Improvement on the decay of crossing numbers
GD'07 Proceedings of the 15th international conference on Graph drawing
Infinite families of crossing-critical graphs with prescribed average degree and crossing number
Journal of Graph Theory
Stars and bonds in crossing-critical graphs
Journal of Graph Theory
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We show that every sufficiently large plane triangulation has a large collection of nested cycles that either are pairwise disjoint, or pairwise intersect in exactly one vertex, or pairwise intersect in exactly two vertices. We apply this result to show that for each fixed positive integer k, there are only finitely many k-crossing-critical simple graphs of average degree at least six. Combined with the recent constructions of crossing-critical graphs given by Bokal, this settles the question of for which numbers q0 there is an infinite family of k-crossing-critical simple graphs of average degree q.