A243251 Number of simple connected graphs with n nodes whose fractional chromatic number is not equal to its (integer) chromatic number.

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

Offset: 1

Author

Travis Hoppe and Anna Petrone, Jun 20 2014

Keywords

• nonn
• more

Comments

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.

Links

• Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
• Eric Weisstein's World of Mathematics, Fractional Chromatic Number

Crossrefs

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

Formula

a(n) = A001349(n) - A243252(n). - Andrew Howroyd, Nov 03 2017

Extensions

Name edited by Michel Marcus, Jan 12 2025