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Spanning subdivisions in Dirac graphs

Part of: Extremal combinatorics Graph theory

Published online by Cambridge University Press:  20 October 2023

Matías Pavez-Signé
Matías Pavez-Signé*
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry, UK
*
Email: matias.pavez-signe@warwick.ac.uk
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Abstract

We show that for every $n\in \mathbb N$ and $\log n\le d\lt n$, if a graph $G$ has $N=\Theta (dn)$ vertices and minimum degree $(1+o(1))\frac{N}{2}$, then it contains a spanning subdivision of every $n$-vertex $d$-regular graph.

Keywords

Subdivisionsdegree conditionsspanning subgraphs

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05D40: Probabilistic methods
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 33 , Issue 1 , January 2024 , pp. 121 - 128
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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