{"citation":{"mla":"Christoph, Micha, et al. “The Hamilton Space of Pseudorandom Graphs.” <i>Journal of Combinatorial Theory Series B</i>, vol. 176, Elsevier, 2025, pp. 254–67, doi:<a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">10.1016/j.jctb.2025.09.002</a>.","chicago":"Christoph, Micha, Rajko Nenadov, and Kalina H Petrova. “The Hamilton Space of Pseudorandom Graphs.” <i>Journal of Combinatorial Theory Series B</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">https://doi.org/10.1016/j.jctb.2025.09.002</a>.","ama":"Christoph M, Nenadov R, Petrova KH. The Hamilton space of pseudorandom graphs. <i>Journal of Combinatorial Theory Series B</i>. 2025;176:254-267. doi:<a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">10.1016/j.jctb.2025.09.002</a>","short":"M. Christoph, R. Nenadov, K.H. Petrova, Journal of Combinatorial Theory Series B 176 (2025) 254–267.","ista":"Christoph M, Nenadov R, Petrova KH. 2025. The Hamilton space of pseudorandom graphs. Journal of Combinatorial Theory Series B. 176, 254–267.","ieee":"M. Christoph, R. Nenadov, and K. H. Petrova, “The Hamilton space of pseudorandom graphs,” <i>Journal of Combinatorial Theory Series B</i>, vol. 176. Elsevier, pp. 254–267, 2025.","apa":"Christoph, M., Nenadov, R., &#38; Petrova, K. H. (2025). The Hamilton space of pseudorandom graphs. <i>Journal of Combinatorial Theory Series B</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">https://doi.org/10.1016/j.jctb.2025.09.002</a>"},"language":[{"iso":"eng"}],"PlanS_conform":"1","intvolume":"       176","main_file_link":[{"url":"https://doi.org/10.1016/j.jctb.2025.09.002","open_access":"1"}],"month":"09","page":"254-267","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"MaKw"}],"abstract":[{"text":"We show that if n is odd and p>=Clog n/n, then with high probability Hamilton cycles in G(n,p) span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph G, that is, a graph G with odd n vertices and minimum degree n/2+C for sufficiently large constant C, span its cycle space.\r\n","lang":"eng"}],"publication":"Journal of Combinatorial Theory Series B","external_id":{"arxiv":["2402.01447"]},"oa_version":"Published Version","_id":"20422","year":"2025","publication_identifier":{"issn":["0095-8956"],"eissn":["1096-0902"]},"day":"26","volume":176,"OA_place":"publisher","date_updated":"2025-10-13T09:39:46Z","project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"author":[{"first_name":"Micha","last_name":"Christoph","full_name":"Christoph, Micha"},{"full_name":"Nenadov, Rajko","last_name":"Nenadov","first_name":"Rajko"},{"id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","full_name":"Petrova, Kalina H","first_name":"Kalina H","last_name":"Petrova"}],"scopus_import":"1","quality_controlled":"1","date_created":"2025-10-05T22:01:34Z","acknowledgement":"This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Image 1 Part of this research was conducted while the author was at Department of Computer Science, ETH Zürich, Switzerland. This author was supported by grant no. CRSII5 173721 of the Swiss National Science Foundation.","article_type":"original","date_published":"2025-09-26T00:00:00Z","doi":"10.1016/j.jctb.2025.09.002","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","title":"The Hamilton space of pseudorandom graphs","OA_type":"hybrid","arxiv":1,"type":"journal_article","corr_author":"1","oa":1,"status":"public"}