- Article: "Linear programming formulation of the vertex colouring problem" Journal: Int. J. of Mathematics in Operational Research, 2010 Vol.2 No.3 pp.259 - 289 Abstract: In this paper, we present a first linear programming (LP) formulation of the vertex colouring problem (VCP). The complexity orders of the number of variables and the number of constraints of the proposed LP are O (δ9·ς3) and O (δ8·ς3), respectively, where δ and ς are the number of vertices and the number of available colours in the VCP instance, respectively. Hence, the proposed model represents a reaffirmation of |P = NP|. First, we develop a bipartite network flow (BNF) based model of the problem. Then, we use a graph-based modelling framework similar to that of Diaby to develop the proposed LP model. A numerical example is used to illustrate the approach. - Inderscience Publishers - linking academia, business and industry through research
- EUDML | Polynomial-time partition of a graph into cliques.