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arXiv · 1312.6213

Subdivisions of a large clique in $C_6$-free graphs

József Balogh·Hong Liu·Maryam Sharifzadeh
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Abstract

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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József Balogh, Hong Liu, Maryam Sharifzadeh. 2014-11-15. Subdivisions of a large clique in $C_6$-free graphs. https://arxiv.org/abs/1312.6213

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