Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Journal of Combinatorial Theory Series B
Spanning trees with many leaves
Journal of Graph Theory
Spanning Trees with Many Leaves in Graphs With Minimum Degree Three
SIAM Journal on Discrete Mathematics
Analytic Combinatorics
Random graphs from a minor-closed class
Combinatorics, Probability and Computing
Growth constants of minor-closed classes of graphs
Journal of Combinatorial Theory Series B
Random unlabelled graphs containing few disjoint cycles
Random Structures & Algorithms
Random graphs with few disjoint cycles
Combinatorics, Probability and Computing
Asymptotic Study of Subcritical Graph Classes
SIAM Journal on Discrete Mathematics
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For fixed positive integers t=3 and k, consider the class of graphs which have at most k disjoint minors isomorphic to a t-star. We shall see that almost all of these graphs contain k vertices such that deleting them leaves a graph with no such minor. This holds for both labelled and unlabelled graphs, and answers a question of Bernardi, Noy and Welsh. We also estimate the asymptotic proportion of graphs in the class which do not have this property.