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A generalization of Noel–Reed–Wu Theorem to signed graphs
Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-02-01 , DOI: 10.1016/j.disc.2020.111833
Wei Wang; Jianguo Qian

Let Σ be a signed graph where two edges joining the same pair of vertices with opposite signs are allowed. The zero-free chromatic number χ(Σ) of Σ is the minimum even integer 2k such that G admits a proper coloring f:V(Σ){±1,±2,,±k}. The zero-free list chromatic number χl(Σ) is the list version of zero-free chromatic number. Σ is called zero-free chromatic-choosable if χl(Σ)=χ(Σ). We show that if Σ has at most χ(Σ)+1 vertices then Σ is zero-free chromatic-choosable. This result strengthens Noel–Reed–Wu Theorem which states that every graph G with at most 2χ(G)+1 vertices is chromatic-choosable, where χ(G) is the chromatic number of G.

更新日期:2020-02-03

 

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