Using the linear space over the binary field that related to a graph G, a sufficient and necessary condition for the chromatic number of G is obtained.
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[2] P. Erdös and A. Hajnal, “Chromatic Number of Finite and Infinite Graphs and Hypergraphs,” Discrete Mathematics, Vol. 53, 1985, pp. 281-285.
[3] N. Biggs, E. Lloyd and R. Wilson, “Graph Theory 1736-1936,” Oxford University Press, Oxford, 1986.