Balogh, József and Katona, Gyula and Linz, William and Tuza, Zsolt (2020) The domination number of the graph defined by two levels of the n-cube, II. EUROPEAN JOURNAL OF COMBINATORICS. ISSN 0195-6698
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Abstract
Consider all k-element subsets and ℓ-element subsets (k>ℓ) of an n-element set as vertices of a bipartite graph. Two vertices are adjacent if the corresponding ℓ-element set is a subset of the corresponding k-element set. Let Gk,ℓ denote this graph. The domination number of Gk,1 was exactly determined by Badakhshian, Katona and Tuza. A conjecture was also stated there on the asymptotic value (n tending to infinity) of the domination number of Gk,2. Here we prove the conjecture, determining the asymptotic value of the domination number [Formula presented]. © 2020 The Authors
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| Additional Information: | Export Date: 24 August 2020 CODEN: EJOCD Funding details: EFOP-3.6.1-16-2016-00015 Funding details: University of Illinois at Urbana-Champaign, UIUC Funding details: National Science Foundation, NSF, DMS-1764123 Funding details: RB 18132 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, NK104183, SNN 129364, SSN117879 Funding text 1: Partially supported by NSF, United States of America Grant DMS-1764123, Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132) and the Langan Scholar Fund (UIUC, United States of America).The research of this author was supported by the National Research, Development and Innovation Office ? NKFIH, Hungary Fund No's SSN117879, NK104183 and K116769.Research supported in part by the National Research, Development and Innovation Office ? NKFIH, Hungary under the grant SNN 129364, and by the Sz?chenyi 2020, Hungary grant EFOP-3.6.1-16-2016-00015. Export Date: 23 September 2020 CODEN: EJOCD Funding details: EFOP-3.6.1-16-2016-00015 Funding details: University of Illinois at Urbana-Champaign, UIUC Funding details: National Science Foundation, NSF, DMS-1764123 Funding details: RB 18132 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, NK104183, SNN 129364, SSN117879 Funding text 1: Partially supported by NSF, United States of America Grant DMS-1764123, Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132) and the Langan Scholar Fund (UIUC, United States of America).The research of this author was supported by the National Research, Development and Innovation Office ? NKFIH, Hungary Fund No's SSN117879, NK104183 and K116769.Research supported in part by the National Research, Development and Innovation Office ? NKFIH, Hungary under the grant SNN 129364, and by the Sz?chenyi 2020, Hungary grant EFOP-3.6.1-16-2016-00015. |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 23 Sep 2020 09:43 |
| Last Modified: | 23 Sep 2020 09:43 |
| URI: | http://real.mtak.hu/id/eprint/114204 |
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