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arXiv · 1812.09396

Tuple domination on graphs with the consecutive-zeros property

María Patricia Dobson·Valeria Leoni·María Inés Lopez Pujato
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Abstract

The $k$-tuple domination problem, for a fixed positive integer $k$, is to find a minimum sized vertex subset such that every vertex in the graph is dominated by at least $k$ vertices in this set. The $k$-tuple domination is NP-hard even for chordal graphs. For the class of circular-arc graphs, its complexity remains open for $k\geq 2$. A $0,1$-matrix has the consecutive 0's property (C0P) for columns if there is a permutation of its rows that places the 0's consecutively in every column. Due to A. Tucker, graphs whose augmented adjancency matrix has the C0P for columns are circular-arc. In this work we study the $k$-tuple domination problem on graphs $G$ whose augmented adjacency matrix has the C0P for columns, for $ 2\leq k\leq |U|+3$, where $U$ is the set of universal vertices of $G$. From an algorithmic point of view, this takes linear time.

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María Patricia Dobson, Valeria Leoni, María Inés Lopez Pujato. 2018-12-21. Tuple domination on graphs with the consecutive-zeros property. https://arxiv.org/abs/1812.09396

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