The domatic number problem in interval graphs

A set of vertices $D$ is a dominating set of a graph $G = ( V,E )$ if every vertex in $V - D$ is adjacent to a vertex in $D$. The domatic number $d ( G )$ of a graph $G = ( V,E )$ is the maximum number $k$ such that $V$ can be partitioned into $k$ disjoint dominating sets $D_1 , \cdots ,D_k $. The m...

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Bibliographic Details
Published inSIAM journal on discrete mathematics Vol. 3; no. 4; pp. 531 - 536
Main Authors TUNG-LIN LU, PEI-HSIN HO, CHANG, G. J
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1990
Subjects
Algorithms
Combinatorics. Ordered structures
Exact sciences and technology
Graphs
Mathematics
Sciences and techniques of general use
Interval graph
NP complete problem
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Summary:A set of vertices $D$ is a dominating set of a graph $G = ( V,E )$ if every vertex in $V - D$ is adjacent to a vertex in $D$. The domatic number $d ( G )$ of a graph $G = ( V,E )$ is the maximum number $k$ such that $V$ can be partitioned into $k$ disjoint dominating sets $D_1 , \cdots ,D_k $. The main purpose of this paper is to give linear algorithms for the domatic number problem in interval graphs. This paper also proves that $d ( G ) = \delta ( G ) + 1$ for any interval graph $G$, where $\delta ( G )$ is the minimum degree of a vertex in $G$.
ISSN:0895-4801
1095-7146
DOI:10.1137/0403045