×

zbMATH — the first resource for mathematics

Edge domatic numbers of complete \(n\)-partite graphs. (English) Zbl 0819.05036
Authors’ abstract: An edge dominating set of a graph is a set of edges \(D\) such that every edge not in \(D\) is adjacent to an edge in \(D\). An edge domatic partition of a graph \(G= (V, E)\) is a collection of pairwise disjoint edge dominating sets of \(G\) whose union is \(E\). The maximum size of an edge domatic partition of \(G\) is called the edge domatic number of \(G\). In this paper we study the edge domatic numbers of complete \(n\)- partite graphs. In particular, we give exact values for the edge domatic numbers of complete 3-partite graphs and balanced complete \(n\)-partite graphs with odd \(n\).

MSC:
05C35 Extremal problems in graph theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bertossi, A.A.: On the domatic number of interval graphs, Inform. Proc. Letters28, 275–280 (1988) · Zbl 0658.68077 · doi:10.1016/0020-0190(88)90173-1
[2] Bonuccelli, M.A.: Dominating sets and domatic number of circular arc graphs, Disc. Appl. Math.12, 203–213 (1985) · Zbl 0579.05051 · doi:10.1016/0166-218X(85)90025-3
[3] Lu, T.L., Ho, P.H., Chang, G.J.: The domatic number problem in interval graphs, SIAM J. Disc. Math.3, 531–536 (1990) · Zbl 0718.05046 · doi:10.1137/0403045
[4] Mitchell, S., Hedetniemi, ST.: Edge domination in trees, Proc. 8th S-? Conf. Combin., Graph Theory and Computing, Congr. Numer.19, 489–509 (1977) · Zbl 0433.05023
[5] Peng, S.L., Chang, M.S.: A new approach for domatic number problem on interval graphs, Proceedings of National Comp. Symp. 1991 R. O. C, 236–241
[6] A. Srinivasa Rao, C. Srinivasa Rao Pandu Rangan: Linear algorithms for domatic number problems on interval graphs. Inform. Proc. Letters33, 29–33 (1989/90) · Zbl 0685.68062 · doi:10.1016/0020-0190(89)90184-1
[7] Yannakakis, M., Gavril, F.: Edge dominating sets in graphs, SIAM J. Appl. Math.38, 364–372 (1980) · Zbl 0455.05047 · doi:10.1137/0138030
[8] Zelinka, B.: Edge-domatic number of a graph, Czech. Math. J.33, 107–110 (1983) · Zbl 0537.05049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.