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 ?
Thanks,Max
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