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Hong Liu (UIUC): Subdivisions of a large clique in $C_6$-free graphs |
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| Joint work with Jozsef Balogh and Maryam Sharifzadeh Mader conjectured that every $C_4$-free graph has a subdivision of a clique of order linear in its average degree. We show that every $C_6$-free graph has such a subdivision of a large clique. We also prove the dense case of Mader's conjecture in a stronger sense, i.e. for every $c$, there is a $c'$ such that every $C_4$-free graph with average degree $cn^{1/2}$ has a subdivision of a clique $K_ell$ with $ell=lfloor c'n^{1/2}rfloor$ where every edge is subdivided exactly $3$ times. |
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| Location : Kalmár Intézet, Árpád tér, szemináriumi szoba | ||||
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