Given any graph X for which we can describe its canonical cliques (that is, typically cliques with large size and simple structure), we can ask whether X has any of the following three related Erdős-Ko-Rado (EKR) properties (see [5] for more details):
• EKR property: the clique number of X equals the size of canonical cliques.
• EKR-module property: the characteristic vector of each maximum clique in X is a Q-linear combination of characteristic vectors of canonical cliques in X.
• strict-EKR property: each maximum clique in X is a canonical clique.
In particular, the Blokhuis' result discussed in Lecture 1 can be viewed as establishing the strict-EKR property of Paley graphs of square order [6].
In this lecture, we overview results on the EKR properties (the three properties described above) of graphs and discuss some further directions.
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