A243251 -id:A243251 - cp's OEIS frontend

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

Travis Hoppe and Anna Petrone, Jun 20 2014

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.

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

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).

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

Name edited by Michel Marcus, Jan 12 2025

A245879 Number of distinct fractional chromatic numbers among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 17, 29, 50

Offset: 1

Travis Hoppe and Anna Petrone, Aug 05 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644, 2014
Eric Weisstein's World of Mathematics, Fractional Chromatic Number

Cf. A243251 (fractional chromatic gap).

cp's OEIS Frontend

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

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