24 research outputs found
A Short Proof that the List Packing Number of any Graph is Well Defined
List packing is a notion that was introduced in 2021 (by Cambie et al.). The
list packing number of a graph , denoted , is the least
such that for any list assignment that assigns colors to each
vertex of , there is a set of proper -colorings of , , with the property whenever and . We present a short proof that for any graph ,
. Interestingly, our proof makes use of Galvin's
celebrated result that the list chromatic number of the line graph of any
bipartite multigraph equals its chromatic number.Comment: 3 page