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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
##### Keywords:
independence; stability; perfect graphs; covering; packing; chordal graphs
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