1,2

The expected clique number of G(n,1/2) is the rational value a(n)/b(n), where b(n) denotes the sequence A006125 (the number of graphs on n labeled nodes). For instance, the expected clique number of G(4,1/2) is a(4)/b(4) = 151/64. G(n,1/2) denotes the random graph on n labeled nodes obtained by choosing, randomly and independently, every pair of nodes {ij} to be an edge with probability 1/2 (Alon, Krivelevich and Sudakov p. 2)

N. Alon, M. Krivelevich and B. Sudakov, Finding a large hidden clique in a random graph, Proc. of the Ninth Annual ACM-SIAM SODA, ACM Press (1998), pp. 594-598. Also: Random Structures and Algorithms 13 (1998), pp. 457-466.

I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, The Maximum Clique Problem, Handbook of Combinatorial Optimization (supplement vol. A), D.-Z. Du and P.M. Pardalos, eds. (1999), pp. 1-74.

Eric Weisstein's World of Mathematics, Clique Number.

Consider the 8 different labeled graphs on 3 nodes: one of the graphs has clique number 1, six of the graphs have clique number 2, and one of the graphs has clique number 3. Hence a(3) = 1*1 + 6*2 + 1*3 = 16.

Cf. A052450, A052451, A052452, A077392, A077393, A077394, A006125.

Adjacent sequences: A086368 A086369 A086370 this_sequence A086372 A086373 A086374

Sequence in context: A006058 A121588 A125281 this_sequence A135753 A091146 A024041

more,nice,nonn

Tim Paulden (timmy(AT)cantab.net), Sep 05 2003