Graphs of low average degree without independent transversals

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Graphs of low average degree without independent transversals
 
Groenland, Carla; Kaiser, Tomáš; Treffers, Oscar; Wales, Matthew
(2023) Journal of Graph Theory, volume 102, issue 2, pp. 374 - 387
(Article)
Abstract
An independent transversal of a graph (Formula presented.) with a vertex partition (Formula presented.) is an independent set of (Formula presented.) intersecting each block of (Formula presented.) in a single vertex. Wanless and Wood proved that if each block of (Formula presented.) has size at least (Formula presented.) and the ... read more
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Keywords: average degree, counterexample, hypergraph, independent transversal, maximum block average degree, Discrete Mathematics and Combinatorics, Geometry and Topology
DOI: https://doi.org/10.1002/jgt.22876
ISSN: 0364-9024
Publisher: Wiley-Liss Inc.
Note: Funding Information: This study was started at the Entropy Compression and Related Methods workshop in March 2021. We extend our thanks to all participants and organisers, and especially to Ross Kang for useful pointers to the literature and many interesting discussions. The first author would like to thank Han Peters for explaining the background related to Möbius transformations. We would like to thank the anonymous reviewers for their helpful comments on this manuscript, and in particular for bringing Remark 5 to our attention. The first author was supported by the European Research Council Horizon 2020 project CRACKNP (grant agreement no. 853234). The second author was supported by project GA20‐09525S of the Czech Science Foundation. Open Access Funding provided by VSNU ‐ Utrecht University (including UMC Utrecht), Netherlands. Funding Information: This study was started at the Entropy Compression and Related Methods workshop in March 2021. We extend our thanks to all participants and organisers, and especially to Ross Kang for useful pointers to the literature and many interesting discussions. The first author would like to thank Han Peters for explaining the background related to Möbius transformations. We would like to thank the anonymous reviewers for their helpful comments on this manuscript, and in particular for bringing Remark 5 to our attention. The first author was supported by the European Research Council Horizon 2020 project CRACKNP (grant agreement no. 853234). The second author was supported by project GA20-09525S of the Czech Science Foundation. Open Access Funding provided by VSNU - Utrecht University (including UMC Utrecht), Netherlands. Publisher Copyright: © 2022 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC.
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