Multiple list coloring of 3‐choice critical graphs
Rongxing Xu, Xuding Zhu · Journal of Graph Theory · 2020
Abstract A graph is called 3‐choice critical if is not 2‐choosable but any proper subgraph is 2‐choosable. A characterization of 3‐choice critical graphs was given by Voigt in 1998. Voigt conjectured that if is a bipartite 3‐choice critical graph, then is ‐choosable for every integer . This conjecture was disproved by Meng et al. in 2017. They showed that if where have the same parity and , or with , then is bipartite 3‐choice critical, but not (4,2)‐choosable. On the other hand, all the other bipartite 3‐choice critical graphs are (4,2)‐choosable. This paper strengthens the result of Meng, Puleo and Zhu and show that all the other bipartite 3‐choice critical graphs are ‐choosable for every integer .