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.

A287007 Number of simple (not necessarily connected) graphs on n vertices whose fractional chromatic number equals its (integer) chromatic number.

Original entry on oeis.org

1, 2, 4, 11, 33, 152, 1006, 11808, 257625, 11018264
Offset: 1

Views

Author

Eric W. Weisstein, May 17 2017

Keywords

Comments

First differs from A198634 (weakly perfect graphs) at a(8). The three 8-node graphs that have equal chromatic and fractional chromatic numbers but are not weakly perfect are the 4-antiprism graph and 50- and 84-Johnson solid skeleton graphs, all of which have clique number 3 but chromatic and fractional chromatic number 4.

Links

Crossrefs

Cf. A198634 (number of weakly perfect graphs on n nodes).
Cf. A243252 (number of simple connected graphs on n nodes with fractional chromatic number equal to chromatic number).
Cf. A287008 (number of simple disconnected graphs on n nodes with fractional chromatic number equal to chromatic number).

Formula

a(n) = A243252(n) + A287008(n).

A287009 Number of connected simple weakly perfect graphs on n vertices.

Original entry on oeis.org

1, 1, 2, 6, 20, 109, 820, 10618, 244536, 10740858, 905808814
Offset: 1

Views

Author

Eric W. Weisstein, May 17 2017

Keywords

Comments

First differs from A243252 (connected simple graphs whose fractional number equals its chromatic number) at a(8). The three (connected) 8-node graphs that have equal chromatic and fractional chromatic numbers but are not weakly perfect are the 4-antiprism graph and 50- and 84-Johnson solid skeleton graphs, all of which have clique number 3 but chromatic and fractional chromatic number 4.

Links

  • F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 4361e42
  • Eric Weisstein's World of Mathematics, Connected Graph
  • Eric Weisstein's World of Mathematics, Weakly Perfect Graph

Crossrefs

Cf. A198634 (not necessarily connected weakly perfect simple graphs on n nodes).
Cf. A287023 (disconnected weakly perfect simple graphs on n nodes).
Cf. A243252 (connected simple graphs whose fractional number equals its chromatic number).

Formula

a(n) = A198634(n) - A287023(n).

Extensions

a(9)-a(10) from Eric W. Weisstein, May 18 2017
a(11) added using tinygraph by Falk Hüffner, Aug 13 2017

A287023 Number of simple disconnected weakly perfect graphs on n vertices.

Original entry on oeis.org

0, 1, 2, 5, 13, 43, 186, 1187, 13006, 270900, 11286208
Offset: 1

Views

Author

Eric W. Weisstein, May 18 2017

Keywords

Comments

First differs from A287008 (number of simple disconnected graphs with equal chromatic and fractional chromatic number) at a(8).

Links

Crossrefs

Cf. A198634 (number of not necessarily connected simple weakly perfect graphs).
Cf. A287009 (number of not connected simple weakly perfect graphs).
Cf. A287008 (number of simple disconnected graphs with equal chromatic and fractional chromatic number).

Formula

a(n) = A198634(n) - A287009(n).

Extensions

a(11) from formula by Falk Hüffner, Aug 13 2017
Showing 1-3 of 3 results.

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

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