[seqfan] Partition into Stroke of the star graph

[Yasu Koh]

    Hi  Se fan
    I recomputed A089243       ,  and I think it is incorrect

    1, 2, 3, 4, 9, 22, 61, 200,    Off SET 0    0 means Phi

    The definition is the following    I think it is the best that Max
Aleksayev gave

    Partition of graph G=(V,E) into strokes is a collection of directed
edge-disjoint trails (viewed as sets of directed edges) in G such that (i)
no two trails can be concatenated into a single one; (ii) the corresponding
undirected edges form a partition of E.

    The definition is for the case of directed , labelled , mirror
symmetric exist    I computed  all cases  that exist eight

            1，1，1，1，2，2， undirected , unlabelled , mirror symmetric doesn't
exist
１，１，３，４，６，１０ directed , unlabelled , mirror symmetric doesn't exist有向。
1，1，1，３，３，1５， undirected , labelled , mirror symmetric doesn't exist
1，2，４，1４，1８， directed , labelled , mirror symmetric doesn't exist
1，1，1，1，2，４， undirected , unlabelled , mirror symmetric exist
1，1，３，４，６，1０， directed , unlabelled , mirror symmetric exist
1，1，1，３，３，2０. undirected , labelled , mirror symmetric existy
１，２，４，１４，１８，８０ directed , labelled , mirror symmetric exist

    I computed these numbers by  hand , could you confirm then  and compute
more term  ?

    For instance , the last case of a(2)

    Four partitions exist as follows:
{1->0->2} , {2->0->1}
｛１－＞０，２－＞０}
｛０－＞１，０－＞２｝
So a(2) = 4



The case of ｎ×1 lattice graph

１，2，８，1７２， directed , labelled , mirror symmetric exist

           n = 3    is    unsolved problem    It is difficult to compute it



    Yasutoshi