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Number of simple connected graphs g whose fractional chromatic number is not equal to its (integer) chromatic number.
2

%I #8 Nov 03 2017 22:21:44

%S 0,0,0,0,1,3,33,496,16464,969293

%N Number of simple connected graphs g whose fractional chromatic number is not equal to its (integer) chromatic number.

%C This implies that there is a gap 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/FractionalChromaticNumber.html">Fractional Chromatic Number</a>

%F a(n) = A001349(n) - A243252(n). - _Andrew Howroyd_, Nov 03 2017

%Y Cf. A243252 (fractional chromatic number is equal to chromatic number)

%K nonn,more

%O 1,6

%A _Travis Hoppe_ and _Anna Petrone_, Jun 20 2014