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In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the third paper of the series, we present duality theorems for a combination of stars and combs: undominated combs. We describe their complementary structures in terms of rayless trees and of tree‐decompositions. Applications include a complete characterisation,...
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs from the well‐known star—comb lemma for infinite graphs. Call a set of vertices in a graph tough in if only finitely many components of meet for every finite vertex set . In this fourth and final paper of the series, we structurally characterise...
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