login
A287007
Number of simple (not necessarily connected) graphs on n vertices whose fractional chromatic number equals its (integer) chromatic number.
3
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
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
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, May 17 2017
STATUS
approved