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

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

Offset

1,6

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

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

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs

Eric Weisstein's World of Mathematics, Fractional Chromatic Number

Formula

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

Crossrefs

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

Sequence in context: A264833 A071405 A234526 * A336539 A221147 A355795

Adjacent sequences: A243248 A243249 A243250 * A243252 A243253 A243254

Keyword

nonn,more

Author

Travis Hoppe and Anna Petrone, Jun 20 2014

Status

approved