Asymptotic properties of random subsets of projective spaces
1982 ◽
Vol 91
(1)
◽
pp. 119-130
◽
Keyword(s):
A random graph on n vertices is a random subgraph of the complete graph on n vertices. By analogy with this, the present paper studies the asymptotic properties of a random submatroid ωr of the projective geometry PG(r−l, q). The main result concerns Kr, the rank of the largest projective geometry occurring as a submatroid of ωr. We show that with probability one, for sufficiently large r, Kr takes one of at most two values depending on r. This theorem is analogous to a result of Bollobás and Erdös on the clique number of a random graph. However, whereas from the matroid theorem one can essentially determine the critical exponent of ωr, the graph theorem gives only a lower bound on the chromatic number of a random graph.
Keyword(s):
2012 ◽
Vol 12
(02)
◽
pp. 1250151
◽
Keyword(s):
1986 ◽
Vol 100
(1)
◽
pp. 167-174
◽
Keyword(s):
2015 ◽
Vol 25
(1)
◽
pp. 76-88
◽
Keyword(s):
2011 ◽
Vol 20
(5)
◽
pp. 763-775
◽
Keyword(s):
1997 ◽
Vol 29
(03)
◽
pp. 567-581
◽
Keyword(s):
Keyword(s):
Keyword(s):