Results 241 to 250 of about 999 (266)

Extremal subgraphs of random graphs

Journal of Graph Theory, 1990
AbstractWe 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, Miklós Simonovits, Joel Spencer   +2 more
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Extremal graphs for the Tutte polynomial

Journal of Combinatorial Theory, Series B, 2022
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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, 1987
AbstractLet 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, 1984
AbstractWe 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, 1977
AbstractThe 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 Mathematics
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Extremal values of the Sombor index in unicyclic and bicyclic graphs

Journal of Mathematical Chemistry, 2021
Juan Rada, Roberto Cruz
exaly  

A Characterization of Edge-Ordered Graphs with Almost Linear Extremal Functions

Combinatorica, 2023
Gabor Tardos, Tardos Gabor
exaly  

Extremal numbers of disjoint triangles in r-partite graphs

Discrete Mathematics, 2023
Junxue Zhang
exaly