A243252 Number of simple connected graphs with n nodes whose fractional chromatic number is equal to its (integer) chromatic number.

1, 1, 2, 6, 20, 109, 820, 10621, 244616, 10747278

Offset: 1

Author

Travis Hoppe and Anna Petrone, Jun 20 2014

Keywords

• nonn
• more

Comments

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.

Links

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

Crossrefs

Cf. A243251 (fractional chromatic number is not equal to chromatic number).

Cf. A287007 (not necessarily connected simple graphs with fractional chromatic number equal to chromatic number).

Cf. A287008 (disconnected simple graphs with fractional chromatic number equal to chromatic number).

Formula

a(n) = A287008(n) - A287007(n).

Extensions

Name edited by Michel Marcus, Jan 12 2025