There is a hypothesis that a non-selfcentric radially-maximal graph of radius r has at least 3r − 1 vertices. Using some recent results we prove this hypothesis for r = 4.

We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of independent random variable with law described by a single cluster. Key-words: Maximal clusters, exponential law, Gumbel distribution, FKG inequality, second m...

For n ≥ 9, we construct maximal partial line spreads for non-singular quadrics of PG(n, q) for every size between approximately (cn + d)(qn−3 + qn−5) log 2q and qn−2, for some small constants c and d. These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gács and Szőnyi. These results also extend spectrum results on maximal pa...