Bing Zhou - Extremal graphs related to star chromatic number and fractional chromatic number

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Bing Zhou - Extremal graphs related to star chromatic number and fractional chromatic number

BING ZHOU, Trent University, Peterborough, Ontario, Canada

Extremal graphs related to star chromatic number and fractional chromatic number

We present results related to two generalizations of the chromatic number of a graph: the star chromatic number $\chi^{\ast}$ and fractional chromatic number $\chi_{f}$ .

In general we have the inequality $2\leq\chi_{f}(G)\leq\chi^{\ast} (G)\leq \chi(G)$ for any graph G. We will study the graphs that have $\chi^{\ast }(G)=\chi(G)$ in relation with other properties of the graphs such as girth and planarity. Similar problems will be considered for the fractional chromatic number as well.