Large Simple d-Cycles in Simplicial Complexes
Combinatorics
2019-10-11 v1
Abstract
We show that the size of the largest simple d-cycle in a simplicial d-complex is at least a square root of 's density. This generalizes a well-known classical result of Erd\H{o}s and Gallai \cite{EG59} for graphs. We use methods from matroid theory applied to combinatorial simplicial complexes.
Cite
@article{arxiv.1910.04605,
title = {Large Simple d-Cycles in Simplicial Complexes},
author = {Roy Meshulam and Ilan Newman and Yuri Rabinovich},
journal= {arXiv preprint arXiv:1910.04605},
year = {2019}
}
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