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Everything about Tree-depth
Numerical invariant of graphs
In graph theory, the tree-depth of a connected undirected graph is a numerical invariant of, the minimum height of a Trémaux tree for a supergraph of. This invariant and its close relatives have gone under many different names in the literature, including vertex ranking number, ordered chromatic number, and minimum elimination tree height; it is also closely related to the cycle rank of directed graphs and the star height of regular languages. Intuitively, where the treewidth of a graph measures how far it is from being a tree, this parameter measures how far a graph is from being a star. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Tree-depthA 5-minute orientation
- Skim a recent paper: Depth-dependent effects of tree species identity on soil microbial community characteristics and multifunctionalityInfluential work since 2022
- Pick up a classic book: Fundamentals of Computer Programming with CSharp Free Book (by Nakov & Co.)The most-reprinted book on the subject
- Read the landmark paper: Tree-depth, subgraph coloring and homomorphism boundsCited 164 times
- Go sideways: Centered coloringA closely related topic
- Go sideways: Star coloringA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Tree-depth, subgraph coloring and homomorphism bounds
Reconfiguration in bounded bandwidth and tree-depth
Tree species partition N uptake by soil depth in boreal forests
Tree Root Growth and Development. I. Form, Spread, Depth and Periodicity
Impact of subsampling and tree depth on random forests
Findings from an in-Depth Annual Tree-Ring Radiocarbon Intercomparison
Radiation-induced narrowing of the tracheobronchial tree: An in-depth analysis
On Low Tree-Depth Decompositions
🆕 Influential since 2022
Depth-dependent effects of tree species identity on soil microbial community characteristics and multifunctionality
Root water uptake depth determines the hydraulic vulnerability of temperate European tree species during the extreme 2018 drought
Modelling of clear water scour depth around bridge piers using M5 tree and ANN-PSO
Coordination between degree of isohydricity and depth of root water uptake in temperate tree species
The influence of soil depth and tree age on soil enzyme activities and stoichiometry in apple orchards
đź“š Books worth reading
Fundamentals of Computer Programming with CSharp Free Book (by Nakov & Co.)Svetlin Nakov · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Centered coloring In graph theory, a centered coloring is a type of graph coloring related to treedepth. The minimum number of colors in a centered coloring of a graph equals…
- Star coloring In the mathematical field of graph theory, a star coloring of a graph G is a (proper) vertex coloring in which every path on four vertices uses at least…
- Shallow minor In graph theory, a shallow minor or limited-depth minor is a restricted form of a graph minor in which the subgraphs that are contracted to form the minor…
- Pathwidth In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number…
- Bounded expansion In graph theory, a family of graphs is said to have bounded expansion if all of its shallow minors are sparse graphs. Many natural families of sparse graphs…
- Dense graph In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected…
- Treewidth In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest…
- Graph minor In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting…