par Cames Van Batenburg, Wouter 
;Huynh, Tony ;Joret, Gwenaël ;Raymond, Jean-Florent
Référence Advances in combinatorics, P2
Publication Publié, 2019-07-01
;Huynh, Tony ;Joret, Gwenaël ;Raymond, Jean-FlorentRéférence Advances in combinatorics, P2
Publication Publié, 2019-07-01
Article révisé par les pairs
| Résumé : | Let H be a planar graph. By a classical result of Robertson and Seymour, there is a function f: N→R such that for all k ϵ N and all graphs G, either G contains k vertex-disjoint subgraphs each containing H as a minor, or there is a subset X of at most f (k) vertices such that G-X has no H-minor. We prove that this remains true with f (k) = ck log k for some constant c = c(H). This bound is best possible, up to the value of c, and improves upon a recent result of Chekuri and Chuzhoy [STOC 2013], who established this with f (k) = ck logd k for some universal constant d. The proof is constructive and yields a polynomial-time O(logOPT)-approximation algorithm for packing subgraphs containing an H-minor. |
