Topological Properties of Event Structures
Résumé
Motivated by the nice labelling problem for event structures, we study the topological properties of the associated graphs. For each n⩾0, we exhibit a graph Gn that cannot occur on an antichain as a subgraph of the graph of an event structure of degree n . The clique complexes of the graphs Gn are disks (n even) and spheres (n odd) in increasing dimensions. We strengthen the result for event structures of degree 3: cycles of length greater than 3 do not occur on antichains as subgraphs. This amounts to saying that the clique complex of the graph of an event structure of degree 3 is acyclic.