Geodesic
Weak degeneracy of planar graphs and locally planar graphs
Ming Han ; Tao Wang ; Jianglin Wu ; Huan Zhou1 ; Xuding Zhu
1Zhejiang Normal University
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d+1)$-list assignment $L$ of $G$, one can construct an $L$ coloring of $G$ by a modified greedy coloring algorithm. It is known that planar graphs of girth 5 are 3-choosable and locally planar graphs are $5$-choosable. This paper strengthens these results and proves that planar graphs of girth 5 are weakly 2-degenerate and locally planar graphs are weakly 4-degenerate.
DOI : 10.37236/11749
Classification : 05C10, 05C15
Mots-clés : weakly \(d\)-degenerate graphs, greedy coloring algorithm

Ming Han    ; Tao Wang    ; Jianglin Wu    ; Huan Zhou  1   ; Xuding Zhu 

1 Zhejiang Normal University 
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     author = {Ming Han and Tao Wang and Jianglin Wu and Huan Zhou and Xuding Zhu},
     title = {Weak degeneracy of planar graphs and locally planar graphs},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {4},
     doi = {10.37236/11749},
     zbl = {1536.05146},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11749/}
}
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Ming Han; Tao Wang; Jianglin Wu; Huan Zhou; Xuding Zhu. Weak degeneracy of planar graphs and locally planar graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11749

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