On the inducibility of cycles

Dan Hefetz; Mykhaylo Tyomkyn

doi:10.1016/j.jctb.2018.04.008

On the inducibility of cycles

Dan Hefetz, Mykhaylo Tyomkyn

Ariel University

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

11 Scopus citations

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)	243-258
Number of pages	16
Journal	Journal of Combinatorial Theory. Series B
Volume	133
DOIs	https://doi.org/10.1016/j.jctb.2018.04.008
State	Published - Nov 2018

Keywords

Cycles
Enumeration
Inducibility
Large graphs

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10.1016/j.jctb.2018.04.008

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title = "On the inducibility of cycles",

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 - Cycles

KW - Enumeration

KW - Inducibility

KW - Large graphs

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JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

On the inducibility of cycles

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