Star coloring of some toroidal graphs
DOI:
https://doi.org/10.55016/s2bb5p30Abstract
A proper coloring of a graph is a star coloring if there is no bicolored path on four vertices, or, equivalently, if every connected subgraph induced by any two color classes is a star. We investigate the star chromatic number $\chi_s$ of some well-known toroidal graphs. First, it is known that for the $d$-dimensional toroidal grid $TG_d$ the star chromatic number is $\mathcal{O}(d^2)$. Some results published in the literature that are applicable to this family of graphs improve this bound to $\mathcal{O}(d^{\frac{3}{2}})$. In this article we show that $\chi_s(TG_d)=\mathcal{O}(d)$. Furthermore, we investigate the star chromatic number of the honeycomb torus $HT(n)$ of size $n$, and show that $\chi_s(HT(n))=4$.Downloads
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Copyright (c) 2026 Kristina Ago, Anna Slivková
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