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author:

Li, Heng (Li, Heng.) [1] | Hou, Jianfeng (Hou, Jianfeng.) [2] (Scholars:侯建锋) | Zhu, Hongguo (Zhu, Hongguo.) [3]

Indexed by:

SCIE

Abstract:

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.

Keyword:

Choosability with union separation Chorded cycle Planar graph Triangle

Community:

  • [ 1 ] [Li, Heng]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350003, Fujian, Peoples R China
  • [ 2 ] [Hou, Jianfeng]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350003, Fujian, Peoples R China
  • [ 3 ] [Zhu, Hongguo]Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

Reprint 's Address:

  • [Zhu, Hongguo]Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

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Source :

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

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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