Branch-decomposition

Branch-decomposition

In graph theory, the branch-decomposition of a graph G=(V,E) is a ternary tree T and a bijection from the set of the leaves of T into E, the set of edges of G. A ternary tree is a tree in which every vertex has degree 1 or 3.

For any edge e of T, the graph T/e is composed of two subtrees T_1 and T_2. These trees induces a bipartition (E_1,E_2) of E which is called an e-separation.

Widths

The width of an "e-separation" is the number of vertices of G incident to an edge of E_1 and an edge of E_2.

The width of a branch-decomposition is the maximum with of an "e-separation".

The branchwidth of G is the minimum width of a "branch-decomposition" of G

References

*citation
last1 = Robertson | first1 = N.
last2 = Seymour | first2 = P.D.
title = Graph minors. X. Obstructions to tree-decomposition
journal = Journal of Combinatorial Theory
volume = 52 | issue = 2 | year = 1991 | pages = 153-190 | doi = 10.1016/0095-8956(91)90061-N
.


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