OEIS is back up

N. J. A. Sloane njas at research.att.com
Mon Aug 20 00:00:34 CEST 2007

On 8/9/07, koh <zbi74583 at boat.zero.ad.jp> wrote:
>     Once I considered about "Strokes" of a graph.>>     See the definition in A089243.>>     Or, "Partition of a graph G into strokes S_i" must satisfy the following conditions.>>     o Union_{i} S_i = H>     o If not{i=j} -> S_i and S_j don't have the same edge>     o If not{i=j} -> S_i U S_j isn't a dipath>     o For all i S_i is a dipath>          Where H is a digraph on G
>     %S A000001 1,2,4,8,16,32,64>     %N A000001 Number of partitions of G_n into "strokes".>                 G_n = {V_n, E_n}, V_n = {v_1, v_2,….v_n}, E_n = {v_1v_2, v2_v_3,….v_{n-1}v_n}>>                  Figure of G_5 : o-o-o-o-o

This particular sequence (which is in OEIS under the name A131517)seems to be a duplicate of A000079...I cannot say for sure until I understand your definition of "partitioninto strokes".For now I have a couple of questions:
1) Shouldn't it be a directed graph likeG_5: o -> o -> o -> o -> oas the partition into strokes is defined only for directed graphs?
2) Could you list all partitions, say, for n=3 ?

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