On the Chromatic Polynomials of Hypergraphs

Abstract

在本文中，我們定義超圖形之強色彩多項式與弱項式，並討論其性質，且證明一個基本定理。我們也證明若H1，H2 為二個q－邊數r－均勻之超圖形，則H1與H2之強色彩多項式與弱多項式均相同。並且若H1，H2 為二個同階的連通套套超圖形，則H1，H2的強色彩多項式相同。

In this paper, we define and develop the properties of the strongly chromatic polynomials and weakly chromatic polynomials of hypergraphs. We prove that strongly chromatic polynomials satisfy the fundamental theorem. We also prove that if H1 and H2 are two q-edge-tree r-uniform hypergraphs, then H1 and H2 are both strongly chromatically equivalent and weakly chromatically equivalent, and we show that if H1 and H2 are connected nested hypergraphs with the same order, then H1 and H2 are strongly chromatically equivalent.