Colorings v.s. list colorings of uniform hypergraphs
Wei Wang, Jianguo Qian, Zhidan Yan

TL;DR
This paper extends known results on list colorings of graphs to hypergraphs, showing that for sufficiently large list sizes, the minimal number of colorings occurs under constant list assignments, using a refined broken cycle theorem.
Contribution
It introduces a refined broken cycle theorem for hypergraphs and establishes a threshold for list assignments where constant lists minimize colorings, extending prior graph results.
Findings
For large k, constant list assignments minimize colorings.
Established a threshold k > 1.135(m-1) for hypergraphs.
Extended graph coloring results to hypergraphs.
Abstract
Let be an integer with and be a connected -uniform hypergraph with edges. By refining the broken cycle theorem for hypergraphs, we show that if then the -list assignment of admitting the fewest colorings is the constant list assignment. This extends the previous results of Donner, Thomassen and the current authors for graphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · graph theory and CDMA systems
