The number of matchings in random regular graphs and bipartite graphs
Journal of Combinatorial Theory Series B
Asymptotic enumeration by degree sequence of graphs of high degree
European Journal of Combinatorics
Asymptotic enumeration of tournaments with a given score sequence
Journal of Combinatorial Theory Series A
Random regular graphs of high degree
Random Structures & Algorithms
Random Regular Graphs of Non-Constant Degree: Independence and Chromatic Number
Combinatorics, Probability and Computing
Random Regular Graphs of Non-Constant Degree: Connectivity and Hamiltonicity
Combinatorics, Probability and Computing
Asymptotic Enumeration of Eulerian Circuits in the Complete Graph
Combinatorics, Probability and Computing
Lower bounds for sense of direction in regular graphs
Distributed Computing
Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums
Journal of Combinatorial Theory Series A
Asymptotic enumeration of dense 0--1 matrices with specified line sums
Journal of Combinatorial Theory Series A
Random dense bipartite graphs and directed graphs with specified degrees
Random Structures & Algorithms
Regular induced subgraphs of a random Graph
Random Structures & Algorithms
Induced subgraphs in sparse random graphs with given degree sequences
European Journal of Combinatorics
| Hi-index | 0.00 |
Let d = (d1, d2,. . ., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph. Although there are many results of this kind, they are restricted to the sparse case with only a few exceptions. Our focus is instead on the case where the average degree is approximately a constant fraction of n. Our approach is the multidimensional saddle-point method. This extends the enumerative work of McKay and Wormald (1990) and is analogous to the theory developed for bipartite graphs by Greenhill and McKay (2009).