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(4, 2)-Choosability of Planar Graphs with Forbidden Structures
2017
Graphs and Combinatorics
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any ℓ∈{3,4,5,6,7}, a planar graph is 4-choosable if it is ℓ-cycle-free. In terms of constraining the list assignment, one refinement of k-choosability is choosability with separation. A graph is (k,s)-choosable
doi:10.1007/s00373-017-1812-5
fatcat:ta5azl3h7nhhfoqnlgnmjmyswm