On the weak 2-coloring number of planar graphs

Ahlam Almulhim, H. A. Kierstead

Research output: Contribution to journalArticlepeer-review

Abstract

For a graph G=(V,E), a total ordering L on V, and a vertex v∈V, let Wcol2[G,L,v] be the set of vertices w∈V for which there is a path from v to w whose length is 0, 1 or 2 and whose L-least vertex is w. The weak 2-coloring number wcol2(G) of G is the least k such that there is a total ordering L on V with |Wcol2[G,L,v]|≤k for all vertices v∈V. We improve the known upper bound on the weak 2-coloring number of planar graphs from 28 to 23. As the weak 2-coloring number is the best known upper bound on the star list chromatic number of planar graphs, this bound is also improved.

Original languageEnglish (US)
Article number112631
JournalDiscrete Mathematics
Volume345
Issue number1
DOIs
StatePublished - Jan 2022

Keywords

  • Planar graph
  • Star chromatic number
  • Weak 2-coloring number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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