Borbenyi, Marton and Csíkvári, Péter (2021) MATCHINGS IN REGULAR GRAPHS: MINIMIZING THE PARTITION FUNCTION. TRANSACTIONS ON COMBINATORICS, 10 (2). pp. 1-23. ISSN 2251-8657
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Official URL: https://doi.org/10.22108/toc.2020.123763.1742
Abstract
For a graph G on v(G) vertices let m(k)(G) denote the number of matchings of size k, and consider the partition function M-G(lambda) = Sigma(n)(k=0)m(k)(G)lambda(k). In this paper we show that if G is a d-regular graph and 0 < lambda < (4d)(-2), then1/v(G) ln M-G(lambda) > 1/v(Kd+1) ln MKd+1(lambda).The same inequality holds true if d = 3 and lambda < 0.3575. More precise conjectures are also given.
| Item Type: | Article |
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| Additional Information: | Export Date: 4 January 2022 Correspondence Address: Borbenyi, M.; Eotvos Lorand UniversityHungary; email: marton.borbenyi@gmail.com Correspondence Address: Csikvari, P.; Alfred Renyi Institute of MathematicsHungary; email: peter.csikvari@gmail.com |
| Uncontrolled Keywords: | Matchings; Regular graphs; Matching polynomial; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 16 Jan 2023 14:39 |
| Last Modified: | 16 Jan 2023 14:39 |
| URI: | http://real.mtak.hu/id/eprint/156616 |
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