On the inducibility of cycles

In 1975 Pippenger and Golumbic proved that any graph on n vertices admits at most 2e(n/k)k induced k-cycles. This bound is larger by a multiplicative factor of 2e than the simple lower bound obtained by a blow-up construction. Pippenger and Golumbic conjectured that the latter lower bound is essenti...

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Bibliografiske detaljer
Main Authors: Hefetz, D, Tyomkyn, M
Format: Journal article
Udgivet: Elsevier 2018
Beskrivelse
Summary:In 1975 Pippenger and Golumbic proved that any graph on n vertices admits at most 2e(n/k)k induced k-cycles. This bound is larger by a multiplicative factor of 2e than the simple lower bound obtained by a blow-up construction. Pippenger and Golumbic conjectured that the latter lower bound is essentially tight. In the present paper we establish a better upper bound of (128e/81) · (n/k)k. This constitutes the first progress towards proving the aforementioned conjecture since it was posed.