Hamiltonicity of random graphs produced by 2-processes
نویسندگان
چکیده
Suppose that a random graph begins with n isolated vertices and evolves by edges being added at random, conditional upon all vertex degrees being at most 2. The final graph is usually 2-regular, but is not uniformly distributed. Some properties of this final graph are already known, but the asymptotic probability of being a Hamilton cycle was not known. We answer this question along with some related questions about cycles arising in the process.
منابع مشابه
Properties of Random Difference Graphs
Generate a bipartite graph on a partitioned set of vertices by randomly assigning to each vertex v some weight w(v) ∈ [0, 1] and adding an edge between vertices u and v (in distinct parts) if and only if w(u)+w(v) > 1; the results of such processes are known as difference graphs. Random difference graphs of a given size can be produced either by uniformly random generation of weights or by choo...
متن کاملRobust Hamiltonicity of random directed graphs
In his seminal paper from 1952 Dirac showed that the complete graph on n ≥ 3 vertices remains Hamiltonian even if we allow an adversary to remove bn/2c edges touching each vertex. In 1960 Ghouila-Houri obtained an analogue statement for digraphs by showing that every directed graph on n ≥ 3 vertices with minimum inand out-degree at least n/2 contains a directed Hamilton cycle. Both statements q...
متن کاملOn the independence number and Hamiltonicity of uniform random intersection graphs
In the uniform random intersection graphs model, denoted by G n,m,λ , to each vertex v we assign exactly λ randomly chosen labels of some label set M of m labels and we connect every pair of vertices that has at least one label in common. In this model, we estimate the independence number α(G n,m,λ), for the wide, interesting range m = n α , α < 1 and λ = O(m 1/4). We also prove the hamiltonici...
متن کاملOn Eulerianity and Hamiltonicity in Annihilating-ideal Graphs
Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either E...
متن کاملLong paths and Hamiltonicity in random graphs
We discuss several classical results about long paths and Hamilton cycles in random graphs and present accessible versions of their proofs, relying on the Depth First Search (DFS) algorithm and the notion of boosters.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 31 شماره
صفحات -
تاریخ انتشار 2007