Topological Properties of Event Structures
Luigi Santocanale · Electronic Notes in Theoretical Computer Science · 2009
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 G n 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 G n 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.