Haven (graph theory)

Haven (graph theory)

In graph theory, if G is a graph, and k ge 0 is an integer, a haven of order k in G is a function assigning to every set X subseteq V(G) with ig|Xig| < k a vertex set of a component of G igackslash X, etaig(Xig), such that if X subseteq Y subseteq V(G) and ig|Yig| < k, then eta(Y) subseteq eta(X).

The Min-max theorem for tree-width states that a graph has a haven of order k if and only if it has tree width at least k - 1.


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