Subgraphs with large degrees and girth
type: Item
instance of: scholarly article
title: Subgraphs with large degrees and girth
zbMATH Open document ID: 0578.05035
DOI: 10.1007/BF02582956
author: Carsten Thomassen
published in: Graphs and Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: The author has studied properties of graphs of large girth and minimum degree 3 in J. Comb. Theory, Ser. B 35, 129-141 (1983; Zbl 0537.05034). \textit{W. Mader} [Math. Ann. 194, 295-312 (1971; Zbl 0213.508)] showed that a graph of minimum degree 3 and large girth is contractible to a graph of large minimum degree. As a counterpart to this result the author suggests the following conjecture: For each pair of natural numbers r,g there exists f(r,g) such that any graph of minimum degree at least f(r,g) contains a subgraph of minimum degree r and girth at least g. The author also mentions a result of \textit{L. Pyber}, \textit{V. Rödl}, and \textit{E. Szemerédi} [Regular subgraphs in graphs with large average degree (to appear)].
reviewed by: H.Kröger
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 3924816
zbMATH Keywords: large girth
zbMATH Keywords: large minimum degree
zbMATH Keywords: subgraph
MaRDI profile type: Publication
cites work: Girth in graphs
full work available at URL: https://doi.org/10.1007/bf02582956
OpenAlex ID: W2028654923
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description: scientific article; zbMATH DE number 3924816