The interval graph completion problem of a graph G includes two class problems： the profile problem and the pathwidth problem, denoted as P（G） and PW（G） respectively, where the profile problem is to find an inter...The interval graph completion problem of a graph G includes two class problems： the profile problem and the pathwidth problem, denoted as P（G） and PW（G） respectively, where the profile problem is to find an interval supergraph with the smallest possible number of edges; the pathwidth problem is to find an interval supergraph with the smallest possible cliquesize. These two class problems have important applications to numerical algebra, VLSI- layout and algorithm graph theory respectively; And they are known to be NP-complete for general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the exact solutions of the profile and the pathwidth of the complete multipartite graph Kn1,n2,...nr （r≥ 2） are determined.展开更多
基金Supported by the Natural Science Foundation of Henan Province（082300460190） Sponsored by Program for Science and Technology Innovation Talents in Universities of Henan Province.
文摘The interval graph completion problem of a graph G includes two class problems： the profile problem and the pathwidth problem, denoted as P（G） and PW（G） respectively, where the profile problem is to find an interval supergraph with the smallest possible number of edges; the pathwidth problem is to find an interval supergraph with the smallest possible cliquesize. These two class problems have important applications to numerical algebra, VLSI- layout and algorithm graph theory respectively; And they are known to be NP-complete for general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the exact solutions of the profile and the pathwidth of the complete multipartite graph Kn1,n2,...nr （r≥ 2） are determined.
