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A note on the minimum number of choosability of planar graphs

Huijuan Wang (), Lidong Wu (), Xin Zhang (), Weili Wu () and Bin Liu ()
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Huijuan Wang: Qingdao University
Lidong Wu: University of Texas at Tyler
Xin Zhang: Xidian University
Weili Wu: Taiyuan University of Technology
Bin Liu: Ocean University of China

Journal of Combinatorial Optimization, 2016, vol. 31, issue 3, No 5, 1013-1022

Abstract: Abstract The problem of minimum number of choosability of graphs was first introduced by Vizing. It appears in some practical problems when concerning frequency assignment. In this paper, we study two important list coloring, list edge coloring and list total coloring. We prove that $$\chi '_{l}(G)=\varDelta $$ χ l ′ ( G ) = Δ and $$\chi ''_{l}(G)=\varDelta +1$$ χ l ′ ′ ( G ) = Δ + 1 for planar graphs with $$\varDelta \ge 8$$ Δ ≥ 8 and without adjacent 4-cycles.

Keywords: Choosability; Planar graph; Cycle; List edge coloring (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-014-9805-2

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