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 …

Every planar graph is known to be acyclically 7‐choosable and is conjectured to be
acyclically 5‐choosable (OV Borodin, DG Fon‐Der‐Flaass, AV Kostochka, E. Sopena, J …

Every planar graph is known to be acyclically 7-choosable and is conjectured to be
acyclically 5-choosable (Borodin et al. 2002 [4]). This conjecture if proved would imply both …

Let G=(V, E) be a graph. A proper vertex coloring of G is acyclic if G contains no bicolored
cycle. Namely, every cycle of G must be colored with at least three colors. G is acyclically L …

The conjecture on acyclic 5‐choosability of planar graphs [Borodin et al., 2002] as yet has
been verified only for several restricted classes of graphs. None of these classes allows 4 …

Every planar graph is known to be acyclically 7-choosable and is conjectured to be
acyclically 5-choosable (Borodin et al. 2002)[7]. This conjecture if proved would imply both …

The conjecture on the acyclic 5-choosability of planar graphs (Borodin et al., 2002) as yet
has been verified only for several restricted classes of graphs: those of girth at least 5 …

A proper vertex coloring of a graph G=(V, E) is acyclic if G contains no bicolored cycle. Given
a list assignment L={L (v)∣ v∈ V} of G, we say G is acyclically L-list colorable if there exists …

Every planar graph is known to be acyclically 7-choosable and is conjectured to be
acyclically 5-choosable (Borodin et al., 2002). This conjecture if proved would imply both …

The acyclic 4-choosability was proved, in particular, for the following planar graphs: without
3-and 4-cycles (Montassier et al., 2006 [29]), without 4-, 5-, and 6-cycles (Montassier et al …