# 1月27日　吕长虹教授学术报告（数统学院）

Let $G=(V, E)$ be a simple connectedgraph. A set $S\subseteq V(G)$ is called a paired-dominating set if everyvertex in $V(G)\setminus S$ has at least one neighbor in $S$ and the subgraphinduced by $S$ contains a perfect matching.

The paired-domination number of $G$,denoted by $\gamma_{pr}(G)$, is the minimum cardinality of a paired-dominatingset of $G$.

In this talk, we will survey thealgorithmic results of paired-domination problem on subclasses of chordalgraphs,  NP-completeness and APX-completenessresults.

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