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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| Формат: | Journal article |
| Опубліковано: |
Elsevier
2018
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| Резюме: | 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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