Results 1 to 10 of about 42,191 (216)
Degree distance and vertex-connectivity
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S Mukwembi
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On vertex-disjoint cycles and degree sum conditions
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ronald J. Gould +2 more
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Vertex degrees close to the average degree
Discrete Mathematics, 2023 Let $G$ be a finite, simple, and undirected graph of order $n$ and average degree $d$. Up to terms of smaller order, we characterize the minimal intervals $I$ containing $d$ that are guaranteed to contain some vertex degree. In particular, for $d_+\in \left(\sqrt{dn},n-1\right]$, we show the existence of a vertex in $G$ of degree between $d_+-\left ...
Johannes Pardey, Dieter Rautenbach
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Toughness and Vertex Degrees [PDF]
Journal of Graph Theory, 2012 AbstractWe study theorems giving sufficient conditions on the vertex degrees of a graph G to guarantee G is t‐tough. We first give a best monotone theorem when , but then show that for any integer , a best monotone theorem for requires at least nonredundant conditions, where grows superpolynomially as .
Douglas Bauer +4 more
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The complexity of degree anonymization by vertex addition [PDF]
Theoretical Computer Science, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robert Bredereck +5 more
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Estimation of vertex degrees in a sampled network [PDF]
2017 51st Asilomar Conference on Signals, Systems, and Computers, 2017 The need to produce accurate estimates of vertex degree in a large network, based on observation of a subnetwork, arises in a number of practical settings. We study a formalized version of this problem, wherein the goal is, given a randomly sampled subnetwork from a large parent network, to estimate the actual degree of the sampled nodes.
Apratim Ganguly, Eric D. Kolaczyk
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On the Vertex-Degree Based Invariants of Digraphs
Discrete Mathematics Letters, 2021 Let $D=(V,A)$ be a digraphs without isolated vertices. A vertex-degree based invariant $I(D)$ related to a real function $φ$ of $D$ is defined as a summation over all arcs, $I(D) = \frac{1}{2}\sum_{uv\in A}{φ(d_u^+,d_v^-)}$, where $d_u^+$ (resp. $d_u^-$) denotes the out-degree (resp. in-degree) of a vertex $u$.
Hanyuan Deng +4 more
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Vertex arboricity and maximum degree
Discrete Mathematics, 1995 This paper mainly proves that if a connected graph \(G= (V,E)\) is neither a cycle nor a clique, then there is a coloring of \(V\) with at most \(\lceil {{\Delta (G)} \over 2} \rceil\) colors such that all color classes induce forests and one of them is a minimum induced forest in \(G\).
Paul A. Catlin, Hong-Jian Lai
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Random graphs with forbidden vertex degrees [PDF]
Random Structures & Algorithms, 2010 AbstractWe study the random graph Gn,λ/n conditioned on the event that all vertex degrees lie in some given subset $ {\cal S} $ of the nonnegative integers. Subject to a certain hypothesis on $ {\cal S} $, the empirical distribution of the vertex degrees is asymptotically Poisson with some parameter $ \hat{\mu} $ given as the root of a certain ...
Geoffrey R. Grimmett, Svante Janson
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Graph realizations: Maximum degree in vertex neighborhoods
Discrete Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amotz Bar-Noy +3 more
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