| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Beijing Inst Technol, Sch Math & Stat, Beijing - Peoples R China
[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[3] Tech Univ Ilmenau, Inst Math, D-98684 Ilmenau - Germany
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | COMBINATORICS PROBABILITY & COMPUTING; v. 30, n. 4, p. 570-590, JUL 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
We prove that, for any t >= 3, there exists a constant c = c(t)> 0 such that any d-regular n-vertex graph with the second largest eigenvalue in absolute value. satisfying lambda <= cd(t-1)/n(t-2) contains vertex-disjoint copies of K-t covering all but at most n(1-1/(8t4)) vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Szabo (Combinatorica 24 (2004), pp. 403-426) that (n, d, lambda)-graphs with n. 3N and lambda <= cd(2)/n for a suitably small absolute constant c > 0 contain triangle-factors. Our arguments combine tools from linear programming with probabilistic techniques, and apply them in a certain weighted setting. We expect this method will be applicable to other problems in the field. (AU) | |
| FAPESP's process: | 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics |
| Grantee: | Guilherme Oliveira Mota |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 14/18641-5 - Hamilton cycles and tiling problems in hypergraphs |
| Grantee: | Jie Han |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |