Colorings versus list colorings of uniform hypergraphs. Issue 3 (15th February 2020)

• Record Type: Journal Article
• Authors: Wang, Wei; Qian, Jianguo; Yan, Zhidan
• Is Part Of: Journal of graph theory. Volume 95:Issue 3(2020)
• Page Start: 384
• Page End: 397
• Publication Date: 2020-02-15
• Subjects: broken cycle -- chromatic polynomial -- list coloring -- uniform hypergraph; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22550
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: Let r be an integer with r ≥ 2 and G be a connected r ‐uniform hypergraph with m edges. By refining the broken cycle theorem for hypergraphs, we show that if k > m − 1 ln ( 1 + 2 ) ≈ 1.135 ( m − 1 ), then the k ‐list assignment of G admitting the fewest colorings is the constant list assignment. This extends the previous results of Donner, Thomassen, and the current authors for graphs.