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A157015
Number of graphs with n vertices having a bipartite connected component.
3
0, 1, 2, 3, 8, 18, 60, 232, 1389, 14174, 291396, 12307993, 1031244083, 166112993730, 50667178220215, 29104660317374991, 31455540471012663839, 64032442292149795841796, 245999865227419158171980939, 1787823661072649054474456291897, 24639596830978183991220162941946112
OFFSET
0,3
LINKS
Tanya Khovanova, Can Someone Be Straight? [From Tanya Khovanova, Sep 23 2009]
FORMULA
a(n) = A000088(n) - A157016(n).
MATHEMATICA
cbs[g_] := Or @@ Map[BipartiteQ, Map[InduceSubgraph[g, # ] &, ConnectedComponents[g]]] Table[Count[Map[cbs, ListGraphs[n]], True], {n, 7}]
(* from Eric W. Weisstein, May 02 2009: *) First do: <<Combinatorica
In[2]:= Table[Count[Graphs[n], _?(Function[g,
Or @@ BipartiteQ /@ (InduceSubgraph[g, # ] & /@
ConnectedComponents[g])])], {n, 8}] // Timing
CROSSREFS
Sequence in context: A073192 A317722 A113183 * A240645 A273754 A242099
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Feb 21 2009
EXTENSIONS
Incorrect comment deleted by N. J. A. Sloane, Feb 22 2009
Terms from a(8) onwards from Max Alekseyev, Feb 22 2009
Offset corrected by Max Alekseyev, Feb 24 2009
a(8) corrected by W. Edwin Clark, May 02 2009; confirmed by Eric W. Weisstein
Corrected by Max Alekseyev and Vladeta Jovovic, May 02 2009
a(18)-a(20) from Max Alekseyev, Jun 24 2013
STATUS
approved