TY - JOUR
TI - Minors in graphs of large θr-girth
AU - Chatzidimitriou, D.
AU - Raymond, J.-F.
AU - Sau, I.
AU - Thilikos, D.M.
JO - European Journal of Combinatorics
PY - 2017
VL - 65
TODO - null
SP - 106-121
PB - INSTAP Academic Press
SN - 0195-6698, 1095-9971
TODO - 10.1016/j.ejc.2017.04.011
TODO - null
TODO - For every r∈N, let θr denote the graph with two vertices and r parallel edges. The θr-girth of a graph G is the minimum number of edges of a subgraph of G that can be contracted to θr. This notion generalizes the usual concept of girth which corresponds to the case r=2. In Kühn and Osthus (2003), Kühn and Osthus showed that graphs of sufficiently large minimum degree contain clique-minors whose order is an exponential function of their girth. We extend this result for the case of θr-girth and we show that the minimum degree can be replaced by some connectivity measurement. As an application of our results, we prove that, for every fixed r, graphs excluding as a minor the disjoint union of kθr’s have treewidth O(k⋅logk). © 2017 Elsevier Ltd
ER -