Linear programming formulation of the vertex colouring problem
نویسنده
چکیده
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 ( 9 ) and O ( 8 ), respectively, where and 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.
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عنوان ژورنال:
- IJMOR
دوره 2 شماره
صفحات -
تاریخ انتشار 2010