A New Approach to Characterise all the Transitive Orientations for an Undirected Graph

摘要

A new approach to find all the transitive orientations for a comparabilitygraph (finite or infinite) is presented. This approach is based on the linkbetween the notion of ``strong'' partitive set and the forcing theory (notionsof simplices and multiplices). A mathematical algorithm is given for the caseof a comparability graph which has only non limit sub-graphs.