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There are many refinements of list coloring, one of which is the choosability with union separation. Let k, s be positive integers and let G be a graph. A (k, k + s)-list assignment of G is a mapping L assigning each vertex v is an element of V (G) a list of colors L(v) such that vertical bar L(v)vertical bar >= k for each vertex v is an element of V (G), and vertical bar L (u) boolean OR L(v)vertical bar >= k + s for each edge uv is an element of E(G). If for each (k, k + s)-list assignment L of G, G admits a proper coloring phi such that phi(v) is an element of L(v) for each v is an element of V (G), then G is (k, k + s)-choosable. Let G be a planar graph. In this paper, we prove: (1) if G contains no chorded 4-cycle, then G is (3, 8)-choosable; (2) if G contains neither intersecting triangles nor intersecting 4-cycles, then G is (3, 6)-choosable.
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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
ISSN: 0126-6705
Year: 2022
Issue: 2
Volume: 45
Page: 851-867
1 . 2
JCR@2022
1 . 0 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:24
JCR Journal Grade:2
CAS Journal Grade:3
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WoS CC Cited Count: 0
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ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 1