منابع مشابه
Hamilton Cycles in Random Geometric Graphs
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This proves a conjecture of Penrose. We also show that in the k-nearest neighbour model, there is a constant κ such that almost every κ-connected graph has a Hamilton cycle.
متن کاملProbability HAMILTON CYCLES IN RANDOM GEOMETRIC GRAPHS
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbour model, there is a constant κ such that almost every κ-connected graph has a Hamilton cycle.
متن کاملHamilton cycles in random lifts of graphs
An n-lift of a graph K, is a graph with vertex set V (K)× [n] and for each edge (i, j) ∈ E(K) there is a perfect matching between {i} × [n] and {j} × [n]. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that there are constants h1, h2 such that if h ≥ h1 then a random n-lift of the complete graph Kh is hamiltonian whp and if ...
متن کاملCompatible Hamilton cycles in random graphs
A graph is Hamiltonian if it contains a cycle passing through every vertex. One of the cornerstone results in the theory of random graphs asserts that for edge probability p logn n , the random graph G(n, p) is asymptotically almost surely Hamiltonian. We obtain the following strengthening of this result. Given a graph G = (V,E), an incompatibility system F over G is a family F = {Fv}v∈V where ...
متن کاملRainbow hamilton cycles in random graphs
One of the most famous results in the theory of random graphs establishes that the threshold for Hamiltonicity in the Erdős-Rényi random graph Gn,p is around p ∼ logn+log logn n . Much research has been done to extend this to increasingly challenging random structures. In particular, a recent result by Frieze determined the asymptotic threshold for a loose Hamilton cycle in the random 3-uniform...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2011
ISSN: 1050-5164
DOI: 10.1214/10-aap718