A characterization of (4,2)‐choosable graphs

Abstract: A graph

G

is emph{

(a, b)

-choosable} if given any list assignment

L

with

| L (v) | = a

for each

v i n V (G)

there exists a function

v a r p h i

such that

v a r p h i (v) i n L (v)

and

| v a r p h i (v) | = b

for all

v i n V (G)

, and whenever vertices

x

and

y

are adjacent

v a r p h i (x) c a p v a r p h i (y) = e m p t y s e t

. Meng, Puleo, and Zhu conjectured a characterization of (4,2)-choosable graphs. We prove their conjecture.

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