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Coloring Bipartite Graphs with Semi-small List Size

Author(s)
Zhu, Daniel G.
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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.
Date issued
2023-01-29
URI
https://hdl.handle.net/1721.1/147879
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Springer International Publishing
Citation
Zhu, Daniel G. 2023. "Coloring Bipartite Graphs with Semi-small List Size."
Version: Final published version

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