Journal of Algorithms
A strengthening of Ben Rebea's lemma
Journal of Combinatorial Theory Series B
Efficient edge domination problems in graphs
Information Processing Letters
Weighted independent perfect domination on cocomparability graphs
Discrete Applied Mathematics
Graph classes: a survey
Generalized domination in chordal graphs
Nordic Journal of Computing
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Implementation of algorithms for maximum matching on nonbipartite graphs.
Implementation of algorithms for maximum matching on nonbipartite graphs.
Efficient total domination in digraphs
Journal of Discrete Algorithms
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An efficiently total dominating set of a graph G is a subset of its vertices such that each vertex of G is adjacent to exactly one vertex of the subset. If there is such a subset, then G is an efficiently total dominable graph (G is etd). In this paper, we prove NP-completeness of the etd decision problem on the class of planar bipartite graphs of maximum degree 3. Furthermore, we give an efficient decision algorithm for T"3-free chordal graphs. A T"3-free graph is a graph that does not contain as induced subgraph a claw, every edge of which is subdivided exactly twice. In the main part, we present three graph classes on which the weighted etd problem is polynomially solvable: claw-free graphs, odd-sun-free chordal graphs (including strongly chordal graphs) and graphs which only induce cycles of length divisible by four (including chordal bipartite graphs). In addition, claw-free etd graphs are shown to be perfect.