Independence Number and Maximal Chromatic Polynomials of Connected Graphs.

Let C k (n) denote the family of all connected graphs of order n with chromatic number k. In this paper we show that the conjecture proposed by Tomescu which if x ≥ k ≥ 4 and G ∈ C k (n) , then P (G , x) ≤ (x) k (x - 1) n - k <graphic href="373_2024_2824_Article_Equ14.gif"></graphic> holds under the additional condition that G has an independent cut-set T of size at most 2 such that the number of components in G \ T is equal to the independence number of G. [ABSTRACT FROM AUTHOR]