Properties of total domination edge-critical graphs
Discrete Applied Mathematics
Discrete Applied Mathematics
Theoretical Computer Science
Enumeration of minimal dominating sets and variants
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Transversals and domination in uniform hypergraphs
European Journal of Combinatorics
Strong Transversals in Hypergraphs and Double Total Domination in Graphs
SIAM Journal on Discrete Mathematics
Nonblocker: parameterized algorithmics for minimum dominating set
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
On α-total domination in graphs
Discrete Applied Mathematics
Hypergraphs with large domination number and with edge sizes at least three
Discrete Applied Mathematics
Transversals and matchings in 3-uniform hypergraphs
European Journal of Combinatorics
Relating the annihilation number and the total domination number of a tree
Discrete Applied Mathematics
Linear hypergraphs with large transversal number and maximum degree two
European Journal of Combinatorics
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The main result of this paper is that every 4-uniform hypergraph on n vertices and m edges has a transversal with no more than (5n + 4m)/21 vertices. In the particular case n = m, the transversal has at most 3n/7 vertices, and this bound is sharp in the complement of the Fano plane. Chvátal and McDiarmid [5] proved that every 3-uniform hypergraph with n vertices and edges has a transversal of size n/2. Two direct corollaries of these results are that every graph with minimal degree at least 3 has total domination number at most n/2 and every graph with minimal degree at least 4 has total domination number at most 3n/7. These two bounds are sharp.