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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| Published in | SIAM journal on discrete mathematics Vol. 3; no. 4; pp. 531 - 536 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.11.1990
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| Online Access | Get full text |
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| Abstract | 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 $G$. |
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| AbstractList | 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 $G$. |
| Author | TUNG-LIN LU CHANG, G. J PEI-HSIN HO |
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| Cites_doi | 10.1016/0020-0190(88)90173-1 10.1016/0166-218X(85)90025-3 10.1137/1.9781611970401 10.1016/S0022-0000(76)80045-1 10.1007/BFb0070371 10.1145/321958.321964 10.1109/TCS.1975.1083994 10.1007/BFb0092276 10.1002/net.3230070305 |
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| Copyright | 1993 INIST-CNRS [Copyright] © 1990 Society for Industrial and Applied Mathematics |
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| Keywords | Interval graph NP complete problem |
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| References | R2 R3 R4 R5 Garey Michael R. (R7) 1979 R6 R10 Golumbic Martin Charles (R8) 1980 R12 R13 Ore Oystein (R11) 1962 Jaeger François (R9) 1972; 274 R1 |
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| Snippet | 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... |
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| Title | The domatic number problem in interval graphs |
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