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arXiv · 1305.2700

On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach

Fei-Huang Chang·Hong-Bin Chen·Jun-Yi Guo·Yu-Pei Huang
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Abstract

This paper studies the on-line choice number on complete multipartite graphs with independence number $m$. We give a unified strategy for every prescribed $m$. Our main result leads to several interesting consequences comparable to known results. (1) If $ k_1-\sum_{p=2}^m(\frac{p^2}{2}-\frac{3p}{2}+1)k_p\geq 0$, where $k_p$ denotes the number of parts of cardinality $p$, then $G$ is on-line chromatic-choosable. (2) If $ |V(G)|\leq\frac{m^2-m+2}{m^2-3m+4}χ(G)$, then $G$ is on-line chromatic-choosable. (3) The on-line choice number of regular complete multipartite graphs $K_{m\star k}$ is at most $(m+\frac{1}{2}-\sqrt{2m-2})k$ for $m\geq 3$.

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Fei-Huang Chang, Hong-Bin Chen, Jun-Yi Guo, Yu-Pei Huang. 2014-12-17. On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach. https://arxiv.org/abs/1305.2700

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