Lieu : CMI, salle ???, le 15/06/06 à 15h00.
Programme :
Summary: Motivated by the nice labeling problem for event structures, we study the topological properties of the associated graphs. For each $n \geq 0$, 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 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.