Planar graphs without intersecting 5-cycles are signed-4-choosable.

A signed graph is a pair (G , σ) , where G is a graph and σ : E (G) → { 1 , − 1 } is a signature of G. A set S of integers is symmetric if i ∈ S implies that − i ∈ S. Given a list assignment L of G , an L -coloring of a signed graph (G , σ) is a coloring f of (G , σ) such that f (v) ∈ L (v) for each v ∈ V (G) and f (u) ≠ σ (u v) f (v) for every edge u v ∈ E (G). The signed choice number ch ± (G) of a graph G is defined to be the minimum integer k such that for any k -list assignment L of G and for any signature σ on G , there is a proper L -coloring of (G , σ). List signed coloring is a generalization of list coloring. However, the difference between signed choice number and choice number can be arbitrarily large. Hu and Wu [Planar graphs without intersecting 5 -cycles are 4 -choosable, Discrete Math. 340 (2017) 1788–1792] showed that every planar graph without intersecting 5-cycles is 4-choosable. In this paper, we prove that ch ± (G) ≤ 4 if G is a planar graph without intersecting 5-cycles, which extends the main result of [D. Hu and J. Wu, Planar graphs without intersecting 5 -cycles are 4 -choosable, Discrete Math. 340 (2017) 1788–1792]. [ABSTRACT FROM AUTHOR]