On graphs with few disjoint t-star minors.
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 gr...
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
2011
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| Shrnutí: | 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. © 2011 Elsevier Ltd. |
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