[seqfan] Partition Into Stroke of Star graph

Yasu Koh kohmotopp at gmail.com
Thu May 18 08:48:17 CEST 2023


 Hi  Seqfan
    I am an amateur mathematician  and my ability of English is not so
good, so it is difficult for me to explain mathematics

      Thought, I made this problem, it is difficult to define it
      Recently, I got the best definition of Partition Into Stroke    It is
the following

    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 (0)
E must be undirected (i) no two trails can be concatenated into a single
one; (ii) the corresponding undirected edges form a partition of E.
One more condition (0) is added
    First of  all, does my definition have  any sense ?
    Did you computed the case of directed, labelled, mirror symmetric ?
    Mine is the following

           1, 2, 4, 8, 50,   ....    OFF SET 0    0 mean  phi


    Could you compute it  and explain the case of n=3 with a figure like
this ?

           1
           0
      2         3

           For n = 3
            103+02, 103+20, 301+02, 301+20, 203+01, 203+10,
           03+02+01, 30+20+10;



    Yasutoshi


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