Topological properties of event structures

Luigi Santocanale (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

Motivated by the nice labeling 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 structure of degree 3: cycles of length greater than 3 do not occur on antichains as subgraphs. This amount to saying that the clique complex of the graph of an event structure of degree 3 is acyclic.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Luigi Santocanale. Topological properties of event structures. GETCO 2006, Geometrical and Topological Methods in Concurrency, Aug 2006, Bonn, Germany. pp.149-160, ⟨10.1016/j.entcs.2009.02.023⟩. ⟨hal-00432038⟩