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Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree

Part of: Extremal combinatorics Graph theory

Published online by Cambridge University Press:  07 December 2016

G. PERARNAU  and
B. REED
G. PERARNAU
Affiliation:
School of Mathematics, University of Birmingham, United Kingdom (e-mail: g.perarnau@bham.ac.uk)
B. REED
Affiliation:
School of Computer Science, McGill University, Canada and Kawarabayashi Large Graph Project, National Institute of Informatics, Japan (e-mail: breed@mcgill.ca)
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Abstract

Let ℱ be a family of graphs and let d be large enough. For every d-regular graph G, we study the existence of a spanning ℱ-free subgraph of G with large minimum degree. This problem is well understood if ℱ does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we study a locally injective analogue of the question.

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05D40: Probabilistic methods
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 3 , May 2017 , pp. 448 - 467
Copyright
Copyright © Cambridge University Press 2016 

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