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- W2954058522 abstract "Given a graph $F$, let $s_t(F)$ be the number of subdivisions of $F$, each with a different vertex set, which one can guarantee in a graph $G$ in which every edge lies in at least $t$ copies of $F$. In 1990, Tuza asked for which graphs $F$ and large $t$, one has that $s_t(F)$ is exponential in a power of $t$. We show that, somewhat surprisingly, the only such $F$ are complete graphs, and for every $F$ which is not complete, $s_t(F)$ is polynomial in $t$. Further, for a natural strengthening of the local condition above, we also characterise those $F$ for which $s_t(F)$ is exponential in a power of $t$." @default.
- W2954058522 created "2019-07-12" @default.
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- W2954058522 date "2016-12-01" @default.
- W2954058522 modified "2023-09-28" @default.
- W2954058522 title "Local conditions for exponentially many subdivisions" @default.
- W2954058522 doi "https://doi.org/10.48550/arxiv.1612.00206" @default.
- W2954058522 hasPublicationYear "2016" @default.
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