par Huynh, Tony 
;Joret, Gwenaël ;Wood, David R.
Référence Combinatorics, probability & computing, 31, 5, page (812-839)
Publication Publié, 2022-01-01
;Joret, Gwenaël ;Wood, David R.Référence Combinatorics, probability & computing, 31, 5, page (812-839)
Publication Publié, 2022-01-01
Article révisé par les pairs
| Résumé : | Given a fixed graph H that embeds in a surface Σ, what is the maximum number of copies of H in an n-vertex graph G that embeds in Σ ? We show that the answer is Θ(nf(H)), where f(H) is a graph invariant called the 'flap-number' of H, which is independent of Σ. This simultaneously answers two open problems posed by Eppstein ((1993) J. Graph Theory 17(3) 409-416.). The same proof also answers the question for minor-closed classes. That is, if H is a K3,t minor-free graph, then the maximum number of copies of H in an n-vertex K3,t minor-free graph G is Θ(nf'(H)), where f′(H) is a graph invariant closely related to the flap-number of H. Finally, when H is a complete graph we give more precise answers. |
