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branch set
Author: Marian Olejar, Jr. Created: Aug/07/2006 Last edit: Aug/07/2006

    graph theory:
    Let G =(V, E) is a graph and H is its subgraph. S = `(V(S), E(S))` is graph.
    
    `V_x` is connected subset of V(S) (`uuu_(V_i, AA i in E(S)) (V_i) = V(S)`, `V_x nn V_y = O/`). In other words it is partition of V(S) into connected vertex subsets.
    For any two vertices x,y `in` S, there is a an edge between `V_x` and `V_y` in H if and only if xy `in` E(S).
    
    H is called MS (H = MS). The sets `V_x` are the branch sets of this MS.
    S is minor of G. S can be obtained from G by deleting all loops and paralel edges and contracting all branch sets into vertices.
    

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Marian Olejar, Jr.: branch set from VeryPrime's Dictionary of mathematics
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