Minors in graphs of large θr-girth

Dimitris Chatzidimitriou, Jean Florent Raymond, Ignasi Sau, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Pages (from-to)106-121
Number of pages16
JournalEuropean Journal of Combinatorics
StatePublished - Oct 2017

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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