TY - JOUR
T1 - Planar graphs are 1-relaxed, 4-choosable
AU - Cushing, William
AU - Kierstead, Henry
N1 - Funding Information:
We thank N. Eaton for introducing us to the problem of relaxed list coloring of planar graphs. We also thank an anonymous referee for many helpful suggestions. The research of the second author is supported in part by NSA grant H98230-08-1-0069.
PY - 2010/7
Y1 - 2010/7
N2 - We show that every planar graph G = (V, E) is 1-relaxed, 4-choosable. This means that, for every list assignment L that assigns a set of at least four colors to each vertex, there exists a coloring f such that f (v) ∈ L (v) for every vertex v ∈ V and each color class f- 1 (α) of f induces a subgraph with maximum degree at most 1.
AB - We show that every planar graph G = (V, E) is 1-relaxed, 4-choosable. This means that, for every list assignment L that assigns a set of at least four colors to each vertex, there exists a coloring f such that f (v) ∈ L (v) for every vertex v ∈ V and each color class f- 1 (α) of f induces a subgraph with maximum degree at most 1.
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U2 - 10.1016/j.ejc.2009.11.013
DO - 10.1016/j.ejc.2009.11.013
M3 - Article
AN - SCOPUS:77951880909
SN - 0195-6698
VL - 31
SP - 1385
EP - 1397
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 5
ER -