[seqfan] Re: Need help with graph sequences

[Brendan McKay]

> From: Tanya Khovanova <mathoflove-seqfan at yahoo.com>
> 
> Hello SeqFans,
> 
> I just submitted two sequences below. My inefficient program counts only the first 6 terms. The problem is that the second sequence exists in the OEIS, but I do not have any good reasons to believe that it is the same as mine, I need the next term to make sure. Can you do that?
> 
> %S A157015 1,2,3,8,18,60
> %N A157015 Number of graphs with n vertices, such that a bipartite connected component exists. 
> %C A157015 There exists a vertex which doesn't belong to a cycle of odd length. 

These two definitions are not the same.  Are they supposed to be?
Maybe you should write "..which isn't connected to a cycle of odd
length".

Brendan.


> %S A157016 0,0,1,3,16,96
> %N A157016 Number of graphs with n vertices such that a bipartite connected component doesn't exist. 
> %C A157016 Any vertex is connected to a cycle of odd length. 
> %t A157016 cbs[g_] := Or @@ Map[BipartiteQ, Map[InduceSubgraph[g, #] &, ConnectedComponents[g]]] Table[Count[Map[cbs, ListGraphs[n]], False], {n, 6}] 
> 
> Thank you in advance,
> Tanya