A proof of Mader's conjecture on large clique subdivisions in C4-free graphs
نویسندگان
چکیده
Given any integers s, t ≥ 2, we show there exists some c = c(s, t) > 0 such that any Ks,t-free graph with average degree d contains a subdivision of a clique with at least cd 1 2 s s−1 vertices. In particular, when s = 2 this resolves in a strong sense the conjecture of Mader in 1999 that every C4-free graph has a subdivision of a clique with order linear in the average degree of the original graph. In general, the widely conjectured asymptotic behaviour of the extremal density of Ks,t-free graphs suggests our result is tight up to the constant c(s, t).
منابع مشابه
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عنوان ژورنال:
- J. London Math. Society
دوره 95 شماره
صفحات -
تاریخ انتشار 2017