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

1,3

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

Table of n, a(n) for n=1..10.

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

Formula

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

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).

Sequence in context: A076323 A241782 A287009 * A366760 A136795 A074115

Adjacent sequences: A243249 A243250 A243251 * A243253 A243254 A243255

Keyword

nonn,more

Author

Travis Hoppe and Anna Petrone, Jun 20 2014

Extensions

Name edited by Michel Marcus, Jan 12 2025

Status

approved