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Integer Roots Chromatic Polynomials of Non-Chordal Graphs and the Prouhet-Tarry-Escott Problem

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In this paper, we give an affirmative answer to a question of Dmitriev concerning the existence of a non-chordal graph with a chordless cycle of order n whose chromatic polynomial has integer roots for a few values of n, extending prior work of Dong et al.

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References

  1. Borwein, P.: Computational Excursions in Analysis and Number Theory. (Springer, New York 2002)

  2. Borwein, P., Ingalls, C.: The Prouhet-Tarry-Escott Problem Revisited. L'Enseignement Mathématique 40, 3–27 (1994)

    Google Scholar 

  3. Dmitriev, I.G.: Weakly cyclic graphs with integral chromatic number. Metody Diskret. Analiz. 34, 3–7 (1980)

    Google Scholar 

  4. Dong, F.M., Koh, K.M.: Non-chordal graphs having integral-root chromatic polynomials. Bull. Combin. Appl. 22, 67–77 (1998)

    Google Scholar 

  5. Dong, F.M., Teo, K.L., Koh, K.M., Hendy, M.D.: Non-chordal graphs having integral-root chromatic polinomials II. Discrete Mathematics 245, 247–253 (2002)

    Google Scholar 

  6. Read, R.C.: Review. Math. Rev. 50, 6909 (1975)

    Google Scholar 

  7. Read, R.C., Tutte, W.T.: Chromatic polynomials. Academic Press, New York, 15–42 (1988)

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Received: April, 2003

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Hernández, S., Luca, F. Integer Roots Chromatic Polynomials of Non-Chordal Graphs and the Prouhet-Tarry-Escott Problem. Graphs and Combinatorics 21, 319–323 (2005). https://doi.org/10.1007/s00373-005-0617-0

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  • DOI: https://doi.org/10.1007/s00373-005-0617-0

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