par Fiorini, Samuel 
;Joret, Gwenaël ;Theis, Dirk ;Wood, David
Référence European journal of combinatorics, 33, 6, page (1226-1245)
Publication Publié, 2012
;Joret, Gwenaël ;Theis, Dirk ;Wood, David Référence European journal of combinatorics, 33, 6, page (1226-1245)
Publication Publié, 2012
Article révisé par les pairs
| Résumé : | A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of the whole graph. More precisely, we describe functions f and h such that every graph with n vertices and average degree at least f(t) contains a K t-model with at most h(t){dot operator}logn vertices. The logarithmic dependence on n is best possible (for fixed t). In general, we prove that f(t)≤2 t-1+ε For t≤4, we determine the least value of f(t); in particular, f(3)=2+ε and f(4)=4+ε For t≤4, we establish similar results for graphs embedded on surfaces, where the size of the K t-model is bounded (for fixed t). © 2012 Samuel Fiorini, Gwenaël Joret, Dirk Oliver Theis, David R. Wood. |
