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A proof of a conjecture of Gyárfás, Lehel, Sárközy and Schelp on Berge-cycles

Part of: Extremal combinatorics Graph theory

Published online by Cambridge University Press:  09 March 2021

G. R. Omidi
G. R. Omidi*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran; School of Mathematics, Institute for Research in Fundamental Sciences (IPM); PO box 19395-5746, Tehran, Iran
*
Email: romidi@cc.iut.ac.ir
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Abstract

It has been conjectured that, for any fixed \[{\text{r}} \geqslant 2\] and sufficiently large n, there is a monochromatic Hamiltonian Berge-cycle in every \[({\text{r}} - 1)\]-colouring of the edges of \[{\text{K}}_{\text{n}}^{\text{r}}\], the complete r-uniform hypergraph on n vertices. In this paper we prove this conjecture.

MSC classification

Primary: 05C65: Hypergraphs
Secondary: 05C45: Eulerian and Hamiltonian graphs 05D10: Ramsey theory
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 5 , September 2021 , pp. 654 - 669
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

This research was partially carried out in the IPM-Isfahan Branch and in part supported by a grant from IPM (no. 92050217).

References

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