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On the Erdős–Sós conjecture for trees with bounded degree

Part of: Graph theory

Published online by Cambridge University Press:  01 February 2021

Guido Besomi ,
Matías Pavez-Signé  and
Maya Stein
Guido Besomi
Affiliation:
Department of Mathematical Engineering, University of Chile
Matías Pavez-Signé
Affiliation:
Department of Mathematical Engineering, University of Chile
Maya Stein*
Affiliation:
Department of Mathematical Engineering, University of Chile
*
*Corresponding author. Email: mstein@dim.uchile.cl
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Abstract

We prove the Erdős–Sós conjecture for trees with bounded maximum degree and large dense host graphs. As a corollary, we obtain an upper bound on the multicolour Ramsey number of large trees whose maximum degree is bounded by a constant.

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05C07: Vertex degrees 05C05: Trees
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 5 , September 2021 , pp. 741 - 761
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

MPS was supported by ANID Doctoral scholarship ANID-PFCHA/Doctorado Nacional/2017-21171132.

‡

MS is also affiliated to Centro de Modelamiento Matemático, Universidad de Chile, UMI 2807 CNRS. MS acknowledges support by CONICYT + PIA/Apoyo a centros científicos y tecnológicos de excelencia con financiamiento Basal, Código AFB170001, and by Fondecyt Regular Grant 1183080.

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