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Rainbow Domination and Related Problems on Some Classes of Perfect Graphs

Abstract : Let $k \in \mathbb {N}$ and let G be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex x with $f(x)=\varnothing $f(x)=∅, $f(N(x)) =[k]$, where [k] denotes the integers ranging from 1 to k. The rainbow domination number $\gamma _{kr}(G)$ is the minimum of $\sum _{x \in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs.
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Wing-Kai Hon, Ton Kloks, Hsiang-Hsuan Liu, Hung-Lung Wang. Rainbow Domination and Related Problems on Some Classes of Perfect Graphs. 1st International Conference on Theoretical Computer Science (TTCS), Aug 2015, Tehran, Iran. pp.121-134, ⟨10.1007/978-3-319-28678-5_9⟩. ⟨hal-01446271⟩

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