The Chromaticity of Certain Complete Multipartite Graphs

نویسندگان

Haixing Zhao

Xueliang Li

Ruying Liu

Chengfu Ye

چکیده

In this paper, we first establish a useful inequality on the minimum real roots of the adjoint polynomials of the complete graphs. By using it, we investigate the chromatic uniqueness of certain complete multipartite graphs. An unsolved problem (i.e., Problem 11), posed by Koh and Teo in Graph and Combin. 6(1990) 259–285, is completely solved by giving it a positive answer. Moreover, many existing results on the chromatic uniqueness of complete multipartite graphs are generalized.

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