GRAPHICAL REALIZATION PROBLEM.

Abstract

Let G be a finite r-graph where two (distinct) vertices are joined by at most r lines and let left bracket G right bracket denote the degree sequence of G. If s is an integer, when it is proved that a degree sequence left bracket K//1 right bracket has a realizing s-graph containing graph G if and only if the sequence left bracket k//i right bracket - left bracket H right bracket is s-realizable for all subgraphs H of G.