Set Graphs. V. On representing graphs as membership digraphs

摘要

An undirected graph is commonly represented as a set of vertices and a set of vertex doubletons; but one can also represent each vertex by a finite set so as to ensure that membership mimics, over these vertex-representing sets, the edge relation of the graph. This alternative modelling, applied to connected claw-free graphs, recently gave crucial clues for obtaining simpler proofs of some of their properties (e.g. Hamiltonicity of the square of the graph).