{"oa_version":"Preprint","issue":"1","title":"Bounded-degree spanning trees in randomly perturbed graphs","quality_controlled":"1","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1507.07960","open_access":"1"}],"language":[{"iso":"eng"}],"intvolume":"        31","date_published":"2017-01-12T00:00:00Z","day":"12","article_type":"original","year":"2017","publisher":"Society for Industrial & Applied Mathematics","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"}],"publication_status":"published","publication":"SIAM Journal on Discrete Mathematics","author":[{"first_name":"Michael","full_name":"Krivelevich, Michael","last_name":"Krivelevich"},{"full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"full_name":"Sudakov, Benny","first_name":"Benny","last_name":"Sudakov"}],"doi":"10.1137/15m1032910","_id":"9590","publication_identifier":{"eissn":["1095-7146"],"issn":["0895-4801"]},"type":"journal_article","extern":"1","volume":31,"date_updated":"2023-02-23T14:02:05Z","oa":1,"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","external_id":{"arxiv":["1507.07960"]},"page":"155-171","status":"public","date_created":"2021-06-22T12:26:25Z","month":"01","citation":{"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>","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>.","short":"M. Krivelevich, M.A. Kwan, B. Sudakov, SIAM Journal on Discrete Mathematics 31 (2017) 155–171.","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.","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>.","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.","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>"},"article_processing_charge":"No"}