Coloring Bipartite Graphs with Semi-small List Size
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26_2022_Article_633.pdf
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515.41 KB
Format
Adobe PDF
Checksum (MD5)
5b28a269ecffb5cd714b6d6c5a2a7b19
Author(s)
Zhu, Daniel G.
Date Issued
January 29, 2023
Publisher
Springer International Publishing
Citation
Zhu, Daniel G. 2023. "Coloring Bipartite Graphs with Semi-small List Size."
Version
Final published version
Abstract
Abstract
Recently, Alon, Cambie, and Kang introduced asymmetric list coloring of bipartite graphs, where the size of each vertex’s list depends on its part. For complete bipartite graphs, we fix the list sizes of one part and consider the resulting asymptotics, revealing an invariant quantity instrumental in determining choosability across most of the parameter space. By connecting this quantity to a simple question on independent sets of hypergraphs, we strengthen bounds when a part has list size 2. Finally, we state via our framework a conjecture on general bipartite graphs, unifying three conjectures of Alon–Cambie–Kang.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00026-022-00633-z
