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

1,2

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

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Chromatic Number

Eric Weisstein's World of Mathematics, Fractional Chromatic Number

Formula

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

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).

Sequence in context: A304125 A082104 A198634 * A369843 A099215 A089407

Adjacent sequences: A287004 A287005 A287006 * A287008 A287009 A287010

Keyword

nonn,more

Author

Eric W. Weisstein, May 17 2017

Status

approved