## Paired domination on interval and circular-arc graphs.(English)Zbl 1124.05070

Summary: We study the paired-domination problem on interval graphs and circular-arc graphs. Given an interval model with endpoints sorted, we give an $$O(m+n)$$ time algorithm to solve the paired-domination problem on interval graphs. The result is extended to solve the paired-domination problem on circular-arc graphs in $$O(m(m+n))$$ time.

### MSC:

 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C85 Graph algorithms (graph-theoretic aspects) 68Q25 Analysis of algorithms and problem complexity 68R10 Graph theory (including graph drawing) in computer science 68W05 Nonnumerical algorithms

### Keywords:

Interval graph; circular-arc graph; paired domination
Full Text:

### References:

 [1] Bonuccelli, M.A., Dominating sets and domination number of circular-arc graphs, Discrete appl. math., 12, 203-213, (1985) · Zbl 0579.05051 [2] Booth, K.S.; Lueker, G.S., Testing for consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms, J. comput. syst. sci., 13, 335-379, (1976) · Zbl 0367.68034 [3] Chang, M.S., Efficient algorithms for the domination problems on interval and circular-arc graphs, SIAM J. comput., 27, 1671-1694, (1998) · Zbl 0911.05051 [4] Eschen, E.M.; Spinrad, J.P., An $$\operatorname{O}(n^2)$$ algorithm for circular-arc graph recognition, (), 128-137 · Zbl 0801.68128 [5] Golumbic, M.C., Interval graphs and related topics, Discrete math., 55, 113-121, (1985) · Zbl 0568.05046 [6] Haynes, T.W.; Hedetniemi, S.T.; Slater, P.J., Domination in graphs: advanced topics, (1998), Marcel Dekker New York · Zbl 0883.00011 [7] Haynes, T.W.; Slater, T.W., Paired-domination in graphs, Networks, 32, 199-206, (1998) · Zbl 0997.05074 [8] Laskar, R.; Pfaff, J.; Hedetniemi, S.M.; Hedetniemi, S.T., On the algorithmic complexity of total domination, SIAM J. algebraic discrete methods, 5, 420-425, (1984) · Zbl 0576.68056 [9] Qiao, H.; Kang, L.Y.; Cardei, M.; Du, D.Z., Paired-domination of trees, J. global optim., 25, 43-54, (2003) · Zbl 1013.05055 [10] Ramalingan, G.; Rangan, C.P., Total domination in interval graphs revisited, Inform. process. lett., 27, 17-21, (1988) · Zbl 0662.68069
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