Results 281 to 290 of about 605,731 (305)
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Journal of Graph Theory, 1993
AbstractAn interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs.
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AbstractAn interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs.
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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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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 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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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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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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