cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A198634 Number of weakly perfect graphs on n nodes.

Original entry on oeis.org

1, 2, 4, 11, 33, 152, 1006, 11805, 257542, 11011758, 917095022, 145164791300
Offset: 1

Views

Author

Eric W. Weisstein, Feb 19 2013

Keywords

Comments

A graph is weakly perfect if it has equal chromatic and clique numbers.
First differs from A287007 (fractional chromatic number equals chromatic number) at a(8). - Eric W. Weisstein, May 17 2017

Links

Crossrefs

Cf. A287007, A287009, A287023.

Formula

a(n) = A287009(n) + A287023(n).

Extensions

a(10) from Eric W. Weisstein, May 17 2017
a(11) added using tinygraph by Falk Hüffner, Aug 13 2017
a(12) added using tinygraph by Jakub Jablonski, Sep 26 2020

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

Original entry on oeis.org

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

Views

Author

Travis Hoppe and Anna Petrone, Jun 20 2014

Keywords

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

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

A287008 Number of disconnected simple graphs on n vertices whose fractional chromatic number equals its chromatic number.

Original entry on oeis.org

0, 1, 2, 5, 13, 43, 186, 1187, 13009, 270986
Offset: 1

Views

Author

Eric W. Weisstein, May 17 2017

Keywords

Links

Crossrefs

Cf. A287007 (number of not-necessarily connected simple graphs on n nodes with fractional chromatic number equal to chromatic number).
Cf. A243252 (number of simple connected graphs on n node with fractional chromatic number equal to chromatic number).

Formula

a(n) = A287007(n) - A243252(n).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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