{"volume":31,"article_type":"original","external_id":{"arxiv":["1507.07960"]},"quality_controlled":"1","day":"12","abstract":[{"text":"We show that for any fixed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding trees into fixed dense graphs and into random graphs, and extends a sizeable body of existing research on randomly perturbed graphs. Specifically, we show that there is c=c(α,Δ) such that if G is an n-vertex graph with minimum degree at least αn, and T is an n-vertex tree with maximum degree at most Δ , then if we add cn uniformly random edges to G, the resulting graph will contain T asymptotically almost surely (as n→∞ ). Our proof uses a lemma concerning the decomposition of a dense graph into super-regular pairs of comparable sizes, which may be of independent interest.","lang":"eng"}],"status":"public","intvolume":"        31","date_updated":"2023-02-23T14:02:05Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.07960"}],"extern":"1","publication_status":"published","publisher":"Society for Industrial & Applied Mathematics","scopus_import":"1","oa":1,"citation":{"apa":"Krivelevich, M., Kwan, M. A., &#38; Sudakov, B. (2017). Bounded-degree spanning trees in randomly perturbed graphs. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/15m1032910\">https://doi.org/10.1137/15m1032910</a>","short":"M. Krivelevich, M.A. Kwan, B. Sudakov, SIAM Journal on Discrete Mathematics 31 (2017) 155–171.","chicago":"Krivelevich, Michael, Matthew Alan Kwan, and Benny Sudakov. “Bounded-Degree Spanning Trees in Randomly Perturbed Graphs.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial &#38; Applied Mathematics, 2017. <a href=\"https://doi.org/10.1137/15m1032910\">https://doi.org/10.1137/15m1032910</a>.","mla":"Krivelevich, Michael, et al. “Bounded-Degree Spanning Trees in Randomly Perturbed Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 31, no. 1, Society for Industrial &#38; Applied Mathematics, 2017, pp. 155–71, doi:<a href=\"https://doi.org/10.1137/15m1032910\">10.1137/15m1032910</a>.","ieee":"M. Krivelevich, M. A. Kwan, and B. Sudakov, “Bounded-degree spanning trees in randomly perturbed graphs,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 31, no. 1. Society for Industrial &#38; Applied Mathematics, pp. 155–171, 2017.","ama":"Krivelevich M, Kwan MA, Sudakov B. Bounded-degree spanning trees in randomly perturbed graphs. <i>SIAM Journal on Discrete Mathematics</i>. 2017;31(1):155-171. doi:<a href=\"https://doi.org/10.1137/15m1032910\">10.1137/15m1032910</a>","ista":"Krivelevich M, Kwan MA, Sudakov B. 2017. Bounded-degree spanning trees in randomly perturbed graphs. SIAM Journal on Discrete Mathematics. 31(1), 155–171."},"type":"journal_article","oa_version":"Preprint","month":"01","issue":"1","title":"Bounded-degree spanning trees in randomly perturbed graphs","_id":"9590","publication_identifier":{"issn":["0895-4801"],"eissn":["1095-7146"]},"doi":"10.1137/15m1032910","article_processing_charge":"No","date_published":"2017-01-12T00:00:00Z","year":"2017","date_created":"2021-06-22T12:26:25Z","publication":"SIAM Journal on Discrete Mathematics","page":"155-171","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","author":[{"first_name":"Michael","full_name":"Krivelevich, Michael","last_name":"Krivelevich"},{"last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan"},{"first_name":"Benny","full_name":"Sudakov, Benny","last_name":"Sudakov"}],"language":[{"iso":"eng"}]}