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Covering, packing and generalized perfection. (English) Zbl 0556.05055
For simple graph \(G=(V,E)\) let T be a family of subsets of V. A T- covering of G is a subset F(T) of T with the property that each vertex \(v\in V\) is in at least one member of F(T); let \(\theta\) (G:T) denote the minimum cardinality of a T-covering of G. A T-packing is a vertex subset P(T) of B with the property that each vertex subset S in T contains at most one vertex in P(T); let \(\alpha\) (G;T) denote the maximum cardinality of a T-packing. Clearly \(\alpha (G:T)\leq \theta (G:T)\) for all G and T.
This paper studies covering and packing problems for \(T_ k\), the family of subtrees of diameter at most k. In particular, classes of chordal graphs for which \(\theta (H:T_ k)=\alpha (H:T_ k)\) for all induced subgraphs H of G are studied.
Reviewer: P.Slater

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C99 Graph theory
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