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See all on WikipediaThe degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph. Degeneracy is also known as the k-core number, width, and linkage, and is essentially the same as the coloring number or Szekeres–Wilf … See more
In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of … See more
The coloring number of a graph G was defined by Erdős & Hajnal (1966) to be the least κ for which there exists an ordering of the vertices of G in which each vertex has fewer than κ … See more
If a graph G is oriented acyclically with outdegree k, then its edges may be partitioned into k forests by choosing one forest for each outgoing edge of each node. Thus, the arboricity of G is at most equal to its degeneracy. In the other direction, an n … See more
A k-core of a graph G is a maximal connected subgraph of G in which all vertices have degree at least k. Equivalently, it is one of the connected components of … See more
Although concepts of degeneracy and coloring number are frequently considered in the context of finite graphs, the original motivation for … See more
Wikipedia text under CC-BY-SA license WEBMar 28, 2019 · Degeneracy arises from the notion that a network or graph with a subgraph of high minimum degree is more robust than a network all of whose subgraphs contain …
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WEBA $k$-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most $k$. But a subgraph $H$ of a graph $G$ can be equal to the full graph …
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WEBJan 1, 2016 · Degeneracy graphs have been applied to help solve the neighborhood problem, to explain why cycling in LP occurs, to develop algorithms to determine two …
WEBA graph is d-degenerate if any subgraph of it contains a vertex of degree at most d. A result of Hayes [5] asserts that any d-degenerate graph with maximum degree at most Dhas …
WEBIn mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; …
WEBCould someone please clarify is the degeneracy of a graph $G$ defined by: $$\max \{\delta(s):s\in S\}$$ where $S$ is the set of all sub-graphs of $G$ including $G$ and …
Degeneracy (graph theory) | Detailed Pedia
WEBThe degeneracy of a graph is the smallest value of k for which it is k-degenerate. The degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of …
WEBABSTRACT. on of so-called degeneracy graphs (DO for short). These are undirected graphs by the means of which the structure and properties of the set of bases a. …
WEBThe degeneracy of a graph is the smallest value of k for which it is k-degenerate. The degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of …
Linear arboricity of degenerate graphs - Chen - 2023 - Journal of …
WEBGiven a positive integer k $k$, a graph G $G$ is k $k$-degenerate if it can be reduced to a trivial graph by successive removal of vertices with a degree at most k $k$. We prove …
How to find graph's degeneracy? - MathOverflow
WEBJan 3, 2017 · The following greedy algorithm determines the degeneracy of a graph $G$ (defined to be the maximum, taken over all subgraphs $H$ of $G$, of the minimum …
Computing the Degeneracy of Large Graphs | SpringerLink
WEBThe degeneracy on an ordering is the maximum outdegree it induces, and the degeneracy of a graph is smallest degeneracy of any node ordering. Small-degeneracy orderings …
WEBIn this paper, we consider three classes of graphs, proving that each considered graph has weak degeneracy at most 3, and each one has list vertex arboricity at most two. …
The Wikipedia definition of the degeneracy of a graph.
WEBI'm trying to understand Wikipedia's definition of "Degeneracy (graph theory)" which says: In graph theory, a k-degenerate graph is an undirected graph in which every subgraph …
WEBHowever, even if graphs seem very similar from a local or a global perspective, they may exhibit different structure at different scales. In this paper, we present a gen-eral …
[2111.05908] Weak degeneracy of graphs - arXiv.org
WEBNov 10, 2021 · Weak degeneracy of graphs. Motivated by the study of greedy algorithms for graph coloring, we introduce a new graph parameter, which we call weak degeneracy. …
Weak degeneracy of graphs - Bernshteyn - Wiley Online Library
WEBMar 8, 2023 · Motivated by the study of greedy algorithms for graph coloring, we introduce a new graph parameter, which we call weak degeneracy. By definition, every d $d$ …
python - Computing the degeneracy of a graph? - Stack Overflow
WEBApr 25, 2012 · I'm looking for a way to compute the degeneracy of a given graph. The wikipedia article outlines a way, but it also stores the degeneracy ordering and I think …
Explanation of graph degeneracy - Mathematics Stack Exchange
WEBJan 20, 2020 · A $k$-degenerate graph is an undirected graph in which every induced subgraph has minimum degree at most $k$. The degeneracy of a graph is the smallest …
Weak degeneracy of regular graphs - ScienceDirect
WEBJun 1, 2024 · Motivated by the study of greedy algorithms for graph coloring, Bernshteyn and Lee introduced a generalization of graph degeneracy, which is called weak …
Space is a latent sequence: A theory of the hippocampus
WEB2 days ago · (A) Learning cognitive maps from sequential sensory observations is challenging because observations do not identify locations uniquely. (B) The cognitive …
combinatorics - Degeneracy of complete bipartite graphs
WEBJul 14, 2022 · By the definition of degeneracy, it is the minimum number $k$ such that the graph is $k$-degenerate. Certainly, $K_{m, n}$ is $max \{m, n\}$ -degenerate. But in …
Simulation-based inference of developmental EEG maturation …
WEB2 days ago · The authors perform simulation-based inference on EEG spectral features with the Spectral Graph Model, and demonstrate that spectral maturation of the brain activity …
Degeneracy of outerplanar graphs - Mathematics Stack Exchange
WEBJun 29, 2012 · The regions in the interior of a maximal outer planar graph form a tree since if there was a cycle, that would surround a vertex, contradicting outerplanarity. Trees …
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