Maximal σ‐polynomials of connected 3‐chromatic graphs

Abstract

AbstractIn the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if ci(G) ≤ ci(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where ci(G) denotes the number of i‐color partitions of G. In this paper the first ⌈ n/2 ⌉ levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003