Turán Problems for Oriented Graphs
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26_2024_687_ReferencePDF.pdf
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Author(s)
Grzesik, Andrzej
Jaworska, Justyna
Kielak, Bartłomiej
Novik, Aliaksandra
Ślusarczyk, Tomasz
Date Issued
February 29, 2024
Journal
Annals of Combinatorics
Publisher
Springer International Publishing
Citation
Grzesik, A., Jaworska, J., Kielak, B. et al. Turán Problems for Oriented Graphs. Ann. Comb. 28, 1303–1322 (2024).
Version
Author's final manuscript
Abstract
A classical Turán problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph H as a subgraph. It is well-known that the chromatic number of H is the graph parameter which describes the asymptotic behavior of this maximum. Here, we consider an analogous problem for oriented graphs, where compressibility plays the role of the chromatic number. Since any oriented graph having a directed cycle is not contained in any transitive tournament, it makes sense to consider only acyclic oriented graphs as forbidden subgraphs. We provide basic properties of the compressibility, show that the compressibility of acyclic oriented graphs with out-degree at most 2 is polynomial with respect to the maximum length of a directed path, and that the same holds for a larger out-degree bound if the Erdős–Hajnal conjecture is true. Additionally, generalizing previous results on powers of paths and arbitrary orientations of cycles, we determine the compressibility of acyclic oriented graphs with restricted distances of vertices to sinks and sources.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00026-024-00687-1
