Graph Powers and Graph Homomorphisms

In this paper, we investigate some basic properties of fractional powers. In this regard, we show that for any non-bipartite graph $G$ and positive rational numbers ${2r+1\over 2s+1} {{\chi(G)}\over{3(\chi(G)-2)}}$ for which $\chi(G^{{2r+1}\over {2s+1}})= 3$.

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