The Isoperimetric Number of Random Regular Graphs
نویسندگان
چکیده
منابع مشابه
Approximating the isoperimetric number of strongly regular graphs
A factor 2 and a factor 3 approximation algorithm are given for the isoperimetric number of Strongly Regular Graphs. One approach involves eigenvalues of the combinatorial laplacian of such graphs. In this approach, both the upper and lower bounds involve the spectrum of the combinatorial laplacian. An interesting inequality is proven between the second smallest and the largest eigenvalue of co...
متن کاملLower Bounds for the Isoperimetric Numbers of Random Regular Graphs
The vertex isoperimetric number of a graph G = (V ,E) is the minimum of the ratio |∂V U |/|U | where U ranges over all nonempty subsets of V with |U |/|V | ≤ u and ∂V U is the set of all vertices adjacent to U but not in U . The analogously defined edge isoperimetric number—with ∂V U replaced by ∂EU , the set of all edges with exactly one endpoint in U —has been studied extensively. Here we stu...
متن کاملThe Chromatic Number of Random Regular Graphs
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.
متن کاملOn the Number of Spanning Trees in Random Regular Graphs
Let d > 3 be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random d-regular graph with n vertices. (The asymptotics are as n → ∞, restricted to even n if d is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary ...
متن کاملOn the chromatic number of random d-regular graphs
In this work we show that, for any fixed d, random d-regular graphs asymptotically almost surely can be coloured with k colours, where k is the smallest integer satisfying d < 2(k−1) log(k−1). From previous lower bounds due to Molloy and Reed, this establishes the chromatic number to be asymptotically almost surely k− 1 or k. If moreover d > (2k−3) log(k−1), then the value k−1 is discarded and ...
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: European Journal of Combinatorics
سال: 1988
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(88)80014-3