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Everything about Dominating set
Subset of a graph's nodes such that all other nodes link to at least one
In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Dominating setA 5-minute orientation
- Skim a recent paper: Twin-Width III: Max Independent Set, Min Dominating Set, and ColoringInfluential work since 2022
- Pick up a classic book: Psychic Warfare - Brain FightingThe most-reprinted book on the subject
- Read the landmark paper: Polynomial-time data reduction for dominating setCited 149 times
- Go sideways: Domatic numberA closely related topic
- Go sideways: Roman dominating setA closely related topic
📖 Definitions
Noun A set of vertices of a graph, such that each vertex in that graph is either in that set or adjacent to a vertex in that set.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Polynomial-time data reduction for dominating set
Constant-time distributed dominating set approximation
Exact algorithms for dominating set
On approximating the minimum independent dominating set
Construction of minimum connected dominating set in wireless sensor networks using pseudo dominating set
Parameterized approximation of dominating set problems
Approximation hardness of edge dominating set problems
The complexity of dominating set reconfiguration
🆕 Influential since 2022
Twin-Width III: Max Independent Set, Min Dominating Set, and Coloring
Nearly tight approximation algorithm for (connected) Roman dominating set
On dominating set of some subclasses of string graphs
A unified greedy approximation for several dominating set problems
A heuristic approximation algorithm of minimum dominating set based on rough set theory
📚 Books worth reading
Psychic Warfare - Brain FightingMark Desade · 1993
Connected Dominating Set Theory And ApplicationsDing-Zhu Du · 2012- 📕Inverse Problems and Zero Forcing for GraphsLeslie Hogben, Jephian C.-H. Lin · 2022
- 📕Golden Anniversary Celebration of the National Association of MathematiciansOmayra Ortega · 2021
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Domatic number In graph theory, a domatic partition of a graph G=(V,E) is a partition of V into disjoint sets V1, V2,...,VK such that each Vi is a dominating set for…
- Roman dominating set In graph theory, a Roman dominating set (RDS) is a special type of dominating set inspired by historical military defense strategies of the Roman Empire…
- Connected dominating set In graph theory, a connected dominating set and a maximum leaf spanning tree are two closely related structures defined on an undirected graph. A connected…
- Global dominating set In graph theory, a global dominating set is a dominating set S of a graph G that is also a dominating set of the complement graph G¯. The global domination…
- Fractional dominating set In graph theory, a fractional dominating set is a generalization of the dominating set concept that allows vertices to be assigned fractional weights between…
- Eternal dominating set Unsolved problem in mathematics Does there exist a graph G such that γ(G) equals γ∞(G) and γ(G) is less than the clique covering number of G? More unsolved…
- Independent dominating set In graph theory, an independent dominating set for a graph G = ( V , E ) {\displaystyle G=(V,E)} is a subset D ⊆ V {\displaystyle D\subseteq V} that is…
- Metric k-center In graph theory, the metric k-center problem or vertex k-center problem is a classical combinatorial optimization problem studied in theoretical computer…