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Characterizations of Strength Extremal Graphs
Graphs and Combinatorics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaofeng Gu 0002 +3 more
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Extremal Graphs on the Rupture Degree
Journal of Interconnection Networks, 2021For a given graph [Formula: see text], by [Formula: see text] and [Formula: see text] denote the order of the largest component and the number of connected components of [Formula: see text], respectively. The rupture degree of [Formula: see text] is an important combinatorial parameters, which defined as [Formula: see text].
Xiaoxiao Qin +3 more
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Ars Comb., 1998
The authors consider the graph weight \(w_\alpha (G)=\sum _{e\in E(G)}w_{\alpha }(e)\), where \(\alpha \neq 0\) is fixed and \(w_{\alpha }(e)=w_{\alpha }(\{x,y\})=(d(x)d(y))^\alpha \) with \(d(x)\) being the degree of \(x\). It is proved that for the Randić weight \(\alpha =-1/2\) (in the first definition in the article the ``\(-\)'' is missing), if ...
Béla Bollobás, Paul Erdös
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The authors consider the graph weight \(w_\alpha (G)=\sum _{e\in E(G)}w_{\alpha }(e)\), where \(\alpha \neq 0\) is fixed and \(w_{\alpha }(e)=w_{\alpha }(\{x,y\})=(d(x)d(y))^\alpha \) with \(d(x)\) being the degree of \(x\). It is proved that for the Randić weight \(\alpha =-1/2\) (in the first definition in the article the ``\(-\)'' is missing), if ...
Béla Bollobás, Paul Erdös
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Extremal subgraphs of random graphs
Journal of Graph Theory, 1990AbstractWe shall prove that if L is a 3‐chromatic (so called “forbidden”) graph, and —Rn is a random graph on n vertices, whose edges are chosen independently, with probability p, and —Bn is a bipartite subgraph of Rn of maximum size, —Fn is an L‐free subgraph of Rn of maximum size, then (in some sense) Fn and Bn are very near to each other: almost ...
László Babai +2 more
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Extremal graphs for the Tutte polynomial
Journal of Combinatorial Theory, Series B, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Extremal graphs in connectivity augmentation
Journal of Graph Theory, 1999\(A(n,k,t)\) is the number of edges required, in the worst case, to augment a \(k\)-connected graph on \(n\) vertices to be \((k+t)\)-connected. The author computes \(A(n,k,t)\) for both edge and directed edge connectivity (\(A(n,k,t) \approx nt/2\)) and determines the extremal graphs. Vertex connectivity is also addressed for \(t=1\).
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Extreme degrees in random graphs
Journal of Graph Theory, 1987AbstractLet G* be a simple undirected graph on n labeled vertices. A general approach to the investigation of the probability distribution of extreme degrees in a random subgraph of G* is given. As an example of the application of the method, we consider the case when G* is a complete bipartite graph.
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An extremal problem on the connectivity of graphs
Networks, 1984AbstractWe solve in this paper a problem proposed by Bi‐weng Zhu at the First Combinatorics and Graph Theory Conference of China. For the minimum degree δ, connectivity k, and line‐connectivity λ of a (p,q) graph, p,q fixed, the maximum values of δ ‐ k, δ ‐ λ, and λ ‐ k are given as well as extremal graphs for which these upper bounds are realized.
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Extremal problems in graph theory
Journal of Graph Theory, 1977AbstractThe aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs.
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Graph Limits and Spectral Extremal Problems for Graphs
SIAM Journal on Discrete MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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