We show that the size of the largest simple d-cycle in a simplicial d-complex K is at least a square root of K’s density. This is a higher dimensional relative of a classical result of Erdős and Gallai , claiming that any graph G contains a simple cycle of size at least linear in G’s density.
Bibliographical noteFunding Information:
Supported in part by the Israel Science Foundation, grant 326/16.
We are very grateful to Jan van den Heuvel from the London School of Economics for an insightful discussion which led to the formulation of the main question addressed in this paper.
Supported in part by the Israel Science Foundation, grant 497/17. Acknowledgements
© 2023, The Hebrew University of Jerusalem.
ASJC Scopus subject areas
- Mathematics (all)