On the inducibility of cycles

Dan Hefetz; Mykhaylo Tyomkyn

doi:10.1016/j.endm.2017.07.012

On the inducibility of cycles

Dan Hefetz
, Mykhaylo Tyomkyn

Ariel University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	593-599
Number of pages	7
Journal	Electronic Notes in Discrete Mathematics
Volume	61
DOIs	https://doi.org/10.1016/j.endm.2017.07.012
State	Published - Aug 2017

Keywords

Inducibility
cycles
extremal problems
multivariate optimisation

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10.1016/j.endm.2017.07.012

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abstract = "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.",

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AB - 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.

KW - Inducibility

KW - cycles

KW - extremal problems

KW - multivariate optimisation

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JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

On the inducibility of cycles

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Keywords

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