We introduce a new variant of graph coloring called correspondence coloring which
generalizes list coloring and allows for reductions previously only possible for ordinary …

After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

Planar graphs without cycles of length from 4 to 7 are proved to be 3-colorable. Moreover, it
is proved that each proper 3-coloring of a face of length from 8 to 11 in a connected plane …

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We provide a “how-to” guide to the use and application of the Discharging Method. Our aim
is not to exhaustively survey results proved by this technique, but rather to demystify the …

A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each
vertex ofGthere is a vertex coloring ofGwhere each vertex receives a color from its own list …

In this survey the following types of colorings of plane graphs are discussed, both in their
vertex and edge versions: facially proper coloring, rainbow coloring, antirainbow coloring …

A graph G is called (k, d)*-choosable if, for every list assignment L satisfying| L (v)|= k for all v
ϵ V (G), there is an L-coloring of G such that each vertex of G has at most d neighbors …

It is known that planar graphs without cycles of length from 4 to 7 are 3-colorable [OV
Borodin, AN Glebov, A. Raspaud, MR Salavatipour, Planar graphs without cycles of length …

Abstract Let d 1, d 2,…, dk be k nonnegative integers. A graph G=(V, E) is (d 1, d 2,…, dk)-
colorable, if the vertex set V of G can be partitioned into subsets V 1, V 2,…, V k such that the …