Hamilton Cycles in Random Graphs: a bibliography

Frieze, Alan

doi:10.48550/arxiv.1901.07139

Cited by 15 publications

(20 citation statements)

References 144 publications

(187 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This generalizes Johansson's result, as well as the result by Bollobás and Frieze, and answers a question by Frieze (see [8], Problem 20).…”

Section: The Random Subgraph Processsupporting

confidence: 89%

Hitting time of edge disjoint Hamilton cycles in random subgraph processes on dense base graphs

Yahav¹,

Krivelevich²

2019

Preprint

View full text Add to dashboard Cite

Consider the random subgraph process on a base graph G on n vertices: a sequenceof random subgraphs of G obtained by choosing an ordering of the edges of G uniformly at random, and by sequentially adding edges to G 0 , the empty graph on the vertex set of G, according to the chosen ordering. We show that if G has one of the following properties:1. There is a positive constant ε > 0 such that δ(G) ≥ 1 2 + ε n; 2. There are some constants α, β > 0 such that every two disjoint subsets U, W of size at least αn have at least β|U ||W | edges between them, and the minimum degree of G is at least (2α + β) • n;or:and λ ≤ c•d 2 n for some absolute constants c, C > 0. then for a positive integer constant k with high probability the hitting time of the property of containing k edge disjoint Hamilton cycles is equal to the hitting time of having minimum degree at least 2k. These results extend prior results by by Johansson and by Frieze and Krivelevich, and answer a question posed by Frieze.

show abstract

“…This generalizes Johansson's result, as well as the result by Bollobás and Frieze, and answers a question by Frieze (see [8], Problem 20).…”

Section: The Random Subgraph Processsupporting

confidence: 89%

Hitting time of edge disjoint Hamilton cycles in random subgraph processes on dense base graphs

Yahav¹,

Krivelevich²

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Proof of Theorem 2.4. Let d = log n/300 and let i 0 , i 1 , i 2 and i 3 be as in (9). Let D 0 , D (v) = 0, and thus, for each 0 ≤ i ≤ i 1 the property in Theorem 2.4 for D i holds trivially.…”

Section: Proof Of Theorem 24 From Theorem 23mentioning

confidence: 99%

“…Independently, Bollobás [4], and Ajtai, Komlós and Szemerédi [1], showed that, in almost every random graph process, the first graph G i with minimum degree at least 2 is Hamiltonian. Further results on the Hamiltonicity of random graphs, including counting and packing results, can be found in Frieze's comprehensive bibliography [9].…”

Section: Introductionmentioning

confidence: 99%

Spanning cycles in random directed graphs

Montgomery

2021

Preprint

View full text Add to dashboard Cite

We show that, in almost every n-vertex random directed graph process, a copy of every possible n-vertex oriented cycle will appear strictly before a directed Hamilton cycle does, except of course for the directed cycle itself. Furthermore, given an arbitrary n-vertex oriented cycle, we determine the sharp threshold for its appearance in the binomial random directed graph. These results confirm, in a strong form, a conjecture of Ferber and Long.

show abstract

“…To illustrate this, we take a closer look at the Erdős-Rényi random graph G n,p which is an n-vertex graph with each edge being present independently with probability p. The existence question of the Hamilton cycle problem is very well understood, cf. the comprehensive survey by Frieze [13]. Let H be the set of Hamiltonian graphs, then for G n,p it holds that (Komlós and Szemerédi [19] and Korshunov [20])…”

Section: Introductionmentioning

confidence: 99%

An O(n) time algorithm for finding Hamilton cycles with high probability

Nenadov,

Steger,

2020

Preprint

View full text Add to dashboard Cite

show abstract

Hamilton Cycles in Random Graphs: a bibliography

Abstract: We provide an annotated bibliography for the study of Hamilton cycles in random graphs and hypergraphs.

Cited by 15 publications

References 144 publications

Hitting time of edge disjoint Hamilton cycles in random subgraph processes on dense base graphs

Hitting time of edge disjoint Hamilton cycles in random subgraph processes on dense base graphs

Spanning cycles in random directed graphs

An O(n) time algorithm for finding Hamilton cycles with high probability

Contact Info

Product

Resources

About