Planar graphs with girth at least 5 are (3,5)-colorable
نویسندگان
چکیده
منابع مشابه
Planar graphs with girth at least 5 are (3, 5)-colorable
A graph is (d1, . . . , dr )-colorable if its vertex set can be partitioned into r sets V1, . . . , Vr where themaximum degree of the graph induced by Vi is at most di for each i ∈ {1, . . . , r}. Let Gg denote the class of planar graphs with minimum cycle length at least g . We focus on graphs in G5 since for any d1 and d2, Montassier and Ochem constructed graphs in G4 that are not (d1, d2)-co...
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We prove a conjecture of Dvořák, Král, Nejedlý, and Škrekovski that planar graphs of girth at least five are square (∆ + 2)-colorable for large enough ∆. In fact, we prove the stronger statement that such graphs are square (∆+2)-choosable and even square (∆+2)-paintable.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.11.012