@article{b4f6a46792db45918186f4e1ea2a9e3d,

title = "Divisible subdivisions",

abstract = "We prove that for every graph (Formula presented.) of maximum degree at most 3 and for every positive integer (Formula presented.) there is a finite (Formula presented.) such that every (Formula presented.) -minor contains a subdivision of (Formula presented.) in which every edge is replaced by a path whose length is divisible by (Formula presented.). For the case of cycles we show that for (Formula presented.) every (Formula presented.) -minor contains a cycle of length divisible by (Formula presented.), and observe that this settles a recent problem of Friedman and the second author about cycles in (weakly) expanding graphs.",

keywords = "complete minors, cycles, divisibility, expanders, subdivisions",

author = "Noga Alon and Michael Krivelevich",

note = "Funding Information: The initial results in this paper were obtained when the second author visited the Department of Mathematics of Princeton University. He would like to thank the department for the hospitality. Research supported in part by NSF grant DMS-1855464, BSF grant 2018267 and the Simons Foundation to Noga Alon. Research supported in part by ISF grant 1261/17 and by USA-Israel BSF grant 2018267 to Michael Krivelevich. Funding Information: The initial results in this paper were obtained when the second author visited the Department of Mathematics of Princeton University. He would like to thank the department for the hospitality. Research supported in part by NSF grant DMS‐1855464, BSF grant 2018267 and the Simons Foundation to Noga Alon. Research supported in part by ISF grant 1261/17 and by USA‐Israel BSF grant 2018267 to Michael Krivelevich. Publisher Copyright: {\textcopyright} 2021 Wiley Periodicals LLC",

year = "2021",

month = dec,

doi = "10.1002/jgt.22716",

language = "English (US)",

volume = "98",

pages = "623--629",

journal = "Journal of Graph Theory",

issn = "0364-9024",

publisher = "Wiley-Liss Inc.",

number = "4",

}