A class $\mathcal{F}$ of graphs has the induced Erdös--Pósa property if there exists a function $f$ such that for every graph $G$ and every positive integer $k$, $G$ contains either $k$ pairwise vertex-disjoint induced subgraphs that belong to $\mathcal{F}$, or a vertex set of size at most $f(k)$ hitting all induced copies of graphs in $\mathcal{F}$. Kim and Kwon in [J. Combin. Theory Ser. B, 145 (2020), pp. 65--112] showed that for a cycle $C_{\ell}$ of length $\ell$, the class of $C_{\ell}$-subdivisions has the induced Erdös--Pósa property if and only if $\ell\le 4$. In this paper, we investigate whether or not the class of $H$-subdivisions has the induced Erdös--Pósa property for other graphs $H$. We completely settle the case when $H$ is a forest or a complete bipartite graph. Regarding the general case, we identify necessary conditions on $H$ for the class of $H$-subdivisions to have the induced Erdös--Pósa property. For this, we provide three basic constructions that are useful for proving that the class of the subdivisions of a graph does not have the induced Erdös--Pósa property. Among remaining graphs, we prove that if $H$ is the diamond, the 1-pan, or the 2-pan, then the class of $H$-subdivisions has the induced Erdös--Pósa property.


  1. Erdös--Pósa property
  2. induced subdivision
  3. packing and covering

MSC codes

  1. 05C75

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Information & Authors


Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 597 - 636
ISSN (online): 1095-7146


Submitted: 12 November 2018
Accepted: 18 January 2021
Published online: 7 April 2021


  1. Erdös--Pósa property
  2. induced subdivision
  3. packing and covering

MSC codes

  1. 05C75



Funding Information

Horizon 2020 Framework Programme https://doi.org/10.13039/100010661 : 648527

Funding Information

Institute for Basic Science https://doi.org/10.13039/501100010446 : IBS-R029-C1

Funding Information

National Research Foundation of Korea https://doi.org/10.13039/501100003725 : NRF-2018R1D1A1B07050294

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