%I #8 May 17 2017 22:40:42
%S 1,1,2,6,20,109,820,10621,244616,10747278
%N Number of simple connected graphs g whose fractional chromatic number is equal to its (integer) chromatic number.
%C This implies that there is no difference between the corresponding integer and linear programs defining fractional colorings. Every simple graph has a fractional chromatic number which is a rational number or integer.
%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticNumber.html">Chromatic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FractionalChromaticNumber.html">Fractional Chromatic Number</a>
%F a(n) = A287008(n) - A287007(n).
%Y Cf. A243251 (fractional chromatic number is not equal to chromatic number).
%Y Cf. A287007 (not necessarily connected simple graphs with fractional chromatic number equal to chromatic number).
%Y Cf. A287008 (disconnected simple graphs with fractional chromatic number equal to chromatic number).
%K nonn,more
%O 1,3
%A _Travis Hoppe_ and _Anna Petrone_, Jun 20 2014