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Everything about Transitive reduction
Copy of a directed graph with redundant edges removed
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible, such that for all pairs v, w of vertices, a (directed) path from v to w in D exists if and only if such a path exists in the reduction. Transitive reductions were introduced by Aho, Garey & Ullman (1972), who provided tight bounds on the computational complexity of constructing them. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Transitive reductionA 5-minute orientation
- Skim a recent paper: Review of: "FinFET nanotransistor, the reduction of scale causes more short channel effects, less gate control, an exponential increase in leakage currents, severe process changes, and power densities"Influential work since 2022
- Pick up a classic book: Assessment of dual-point drag reduction for an executive-jet modified airfoil sectionThe most-reprinted book on the subject
- Read the landmark paper: Alloys of platinum and early transition metals as oxygen reduction electrocatalystsCited 3,163 times
- Go sideways: Directed acyclic graphA closely related topic
- Go sideways: Glossary of graph theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Alloys of platinum and early transition metals as oxygen reduction electrocatalysts
The Transitive Reduction of a Directed Graph
On primitivity and reduction for flag-transitive symmetric designs
Transitive reduction of citation networks
TRANSWESD: inferring cellular networks with transitive reduction
Reduction for primitive flag-transitive (v, k, 4)-symmetric designs
On the calculation of transitive reduction—closure of orders
An algorithm for transitive reduction of an acyclic graph
🆕 Influential since 2022
Review of: "FinFET nanotransistor, the reduction of scale causes more short channel effects, less gate control, an exponential increase in leakage currents, severe process changes, and power densities"
Reduction for flag-transitive symmetric designs with k > λ(λ − 2)
Reduction for block-transitive t-$$(k^2,k,\lambda )$$ designs
Decreasing graph complexity with transitive reduction to improve temporal graph classification
Interdisciplinarity revealed by transitive reduction of citation networks
📚 Books worth reading
- 📕Assessment of dual-point drag reduction for an executive-jet modified airfoil sectionDennis O. Allison · 1996
- 📕Hybrid laminar flow control experiments in the NASA - Ames, 11-foot tunnelW. S. Saric · 1995
- 📕Nanostructured CatalystsFrederik N. Naraschewski, Robert K. Grasselli · 2011
The mechanisms of reactions at transition metal sitesRichard A. Henderson · 1997
Metal sites in proteins and modelsH. A. O. Hill · 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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