Abstract
The notion of the star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel by subdivisions, their star chromatic numbers being 2+2/(2n + 1), 2+3/(3n + 1), and 2+3(3n−1), respectively. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n, which is a generalization of one result of Gao et al.
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Li, D.M. The Star Chromatic Numbers of Some Planar Graphs Derived from Wheels. Acta Math Sinica 18, 173–180 (2002). https://doi.org/10.1007/s101140100142
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DOI: https://doi.org/10.1007/s101140100142