A287007 Number of simple (not necessarily connected) graphs on n vertices whose fractional chromatic number equals its (integer) chromatic number.

1, 2, 4, 11, 33, 152, 1006, 11808, 257625, 11018264

Offset: 1

Author

Eric W. Weisstein, May 17 2017

Keywords

• nonn
• more

Comments

First differs from A198634 (weakly perfect graphs) at a(8). The three 8-node graphs that have equal chromatic and fractional chromatic numbers but are not weakly perfect are the 4-antiprism graph and 50- and 84-Johnson solid skeleton graphs, all of which have clique number 3 but chromatic and fractional chromatic number 4.

Links

• Eric Weisstein's World of Mathematics, Chromatic Number
• Eric Weisstein's World of Mathematics, Fractional Chromatic Number

Crossrefs

Cf. A198634 (number of weakly perfect graphs on n nodes).

Cf. A243252 (number of simple connected graphs on n nodes with fractional chromatic number equal to chromatic number).

Cf. A287008 (number of simple disconnected graphs on n nodes with fractional chromatic number equal to chromatic number).

Formula

a(n) = A243252(n) + A287008(n).