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Komlós’s tiling theorem via graphon covers
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Hladký, Jan, Hu, Ping and Piguet, Diana (2019) Komlós’s tiling theorem via graphon covers. Journal of Graph Theory, 90 (1). pp. 24-45. doi:10.1002/jgt.22365 ISSN 1097-0118.
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Official URL: https://doi.org/10.1002/jgt.22365
Abstract
Komlós [Komlós: Tiling Turán Theorems, Combinatorica, 2000] determined the asymptotically optimal minimum‐degree condition for covering a given proportion of vertices of a host graph by vertex‐disjoint copies of a fixed graph H, thus essentially extending the Hajnal–Szemerédi theorem that deals with the case when H is a clique. We give a proof of a graphon version of Komlós's theorem. To prove this graphon version, and also to deduce from it the original statement about finite graphs, we use the machinery introduced in [Hladký, Hu, Piguet: Tilings in graphons, arXiv:1606.03113]. We further prove a stability version of Komlós's theorem.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Graph theory | ||||||||||||
| Journal or Publication Title: | Journal of Graph Theory | ||||||||||||
| Publisher: | John Wiley & Sons Ltd. | ||||||||||||
| ISSN: | 1097-0118 | ||||||||||||
| Official Date: | January 2019 | ||||||||||||
| Dates: |
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| Volume: | 90 | ||||||||||||
| Number: | 1 | ||||||||||||
| Page Range: | pp. 24-45 | ||||||||||||
| DOI: | 10.1002/jgt.22365 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Date of first compliant deposit: | 22 March 2018 | ||||||||||||
| Date of first compliant Open Access: | 12 June 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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