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Finding any given 2-factor in sparse pseudorandom graphs efficiently

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Autor(es):
Han, Jie ; Kohayakawa, Yoshiharu ; Morris, Patrick ; Person, Yury
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: JOURNAL OF GRAPH THEORY; v. 96, n. 1, p. 22-pg., 2020-05-05.
Resumo

Given an n-vertex pseudorandom graph G and an n-vertex graph H with maximum degree at most two, we wish to find a copy of H in G, that is, an embedding phi:V(H)-> V(G) so that phi(u)phi(v)is an element of E(G) for all uv is an element of E(H). Particular instances of this problem include finding a triangle-factor and finding a Hamilton cycle in G. Here, we provide a deterministic polynomial time algorithm that finds a given H in any suitably pseudorandom graph G. The pseudorandom graphs we consider are (p,lambda)-bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, omega(pn). A (p,lambda)-bijumbled graph is characterised through the discrepancy property: |e(A,B)-p|A||B||<lambda|A||B| for any two sets of vertices A and B. Our condition lambda=O(p2n/logn) on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption-reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications. (AU)

Processo FAPESP: 14/18641-5 - Circuitos hamiltonianos e problemas de ladrilhamento em hipergrafos
Beneficiário:Jie Han
Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 13/03447-6 - Estruturas combinatórias, otimização e algoritmos em Teoria da Computação
Beneficiário:Carlos Eduardo Ferreira
Modalidade de apoio: Auxílio à Pesquisa - Temático