Integer Root Chromatic Polynomials of Nonchordal Graphs and the Prouhet-Tarry-Escott 

Problem

Florian Luca ^[1]

Instituto de Matemáticas, Unidad Morelia, UNAM, Mexico

fluca@matmor.unam.mx

Abstract. Full Text PDF

Let be a connected simple graph. It is known that if is chordal (i.e., contains no chordless cycles), then its chromatic polynomial has integer roots. However, there are examples of nonchordless graphs whose chromatic polynomials still has integer roots, the smallest such being the Read graph. Recently, Dong, Teo, Koh and Hendy gave a general construction which, in certain instances, specilized to produce examples of graphs with a nonchordal cycle of length for , and such that its chromatic polynomial has integer roots. In my talk, I will relate their construction to a famous problem in number theory called the Prouhet-Tarry-Escott problem, and extend their result to

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^[1] This is joint work with Santos Hernández.