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Number of simple connected graphs g whose fractional chromatic number is equal to its (integer) chromatic number.
4

%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