[seqfan] inverse Euler transforms needed

Brendan McKay Brendan.McKay at anu.edu.au
Mon Mar 12 01:50:48 CET 2018

Hi Seqfans,  I have just extended four sequences of graph counts.

Since these graph classes are closed under disjoint union, the 
corresponding sequence of connected graph counts can be obtained using 
an inverse euler transform (but don't take my word for it).

Can someone with more spare time on their hands than I have please 
extend the connected graph counts?  Some cross-referencing between the 
two sequences in each pair is missing too.

The sequences are:

Graphs without 3-cycles or 4-cycles:   A006787->A126757

Squarefree bipartite graphs:  A138347->seems not to be present,
starts 1,1,1,2,3,7,12,30,64,177,457,1403

Graphs without 4-cycles:   A006786->A077269

Perfect graphs:   A052431->A052433

Thanks, Brendan.

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