Upper Bound for the Coefficients of Chromatic polynomials

نویسندگان

  • Shu-Chiuan Chang
  • C. N. Yang
چکیده

This paper describes an improvement in the upper bound for the magnitude of a coefficient of a term in the chromatic polynomial of a general graph. If ar is the coefficient of the q r term in the chromatic polynomial P (G, q), where q is the number of colors, then we find ar ≤ ( e v−r ) − ( e−g+2 v−r−g+2 ) + ( e−kg−g+2 v−r−g+2 ) − ∑kg−lg n=1 ∑lg−1 m=1 ( e−g+1−n−m v−r−g ) − δg,3 ∑kg+l ∗ g+1 −lg n=1 ( e−lg−g+1−n v−r−g ) , where kg is the number of circuits of length g and lg and l ∗ g+1 are certain numbers defined in the text. key words: chromatic polynomial

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تاریخ انتشار 2001