Browsing Combinatorics and Optimization by Subject "random graphs"
Now showing items 1-4 of 4
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Core Structures in Random Graphs and Hypergraphs
(University of Waterloo, 2013-08-30)The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, ... -
Diameter and Rumour Spreading in Real-World Network Models
(University of Waterloo, 2015-04-20)The so-called 'small-world phenomenon', observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network's size, typically growing as a ... -
Goldberg's conjecture is true for random multigraphs
(Elsevier, 2019-09)In the 70s, Goldberg, and independently Seymour, conjectured that for any multigraph G, the chromatic index χ′(G) satisfies χ′(G) ≤ max{∆(G)+1,⌈ρ(G)⌉}, where ρ(G) = max\{\frac {e(G[S])}{\lfloor|S|/2\rfloor} \mid S\subseteq ... -
On the Strongly Connected Components of Random Directed Graphs with Given Degree Sequences
(University of Waterloo, 2016-08-24)A strongly connected component of a directed graph G is a maximal subgraph H of G such that for each pair of vertices u and v in H, there is a directed path from u to v and a directed path from v to u in H. A strongly ...