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- W2055841009 abstract "Given a graph $G = ( V,E )$, let $T_k = ( V ( T_k ), E ( T_k ) )$ be a tree of diameter $leqq k$ that is a partial graph of G. Let $mathcal{J}_k $ be the set of $V ( T_k )$ for all such G. $T_k $. We consider covering and packing problems defined with respect to G. $mathcal{J}_k $, for all integers $kgeqq 1$. $theta ( G:mathcal{J}_k )$ is the minimum number of elements of $mathcal{J}_k $ that cover V, and $alpha ( G:mathcal{J}_k )$ is the maximum size of a $P subseteq V$ such that no element of $mathcal{J}_k $ contains more than one element of P. In particular, $theta ( G:mathcal{J}_1 )$ is the edge covering number of G, $theta ( G:mathcal{J}_2 )$ is the domination number of G, and $alpha ( G:mathcal{J}_1 )$ is the stability number of G. We study classes of chordal graphs for which $theta ( H:mathcal{J}_k ) = alpha ( H:mathcal{J}_k )$ for all induced subgraphs H of G. We also give simple algorithms for solving these problems on some classes of graphs. These results are applicable to location problems." @default.
- W2055841009 created "2016-06-24" @default.
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- W2055841009 date "1985-01-01" @default.
- W2055841009 modified "2023-09-23" @default.
- W2055841009 title "Covering, Packing and Generalized Perfection" @default.
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- W2055841009 doi "https://doi.org/10.1137/0606012" @default.
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