On MAXCUT in strictly supercritical random graphs, and coloring of random graphs and random tournaments
نویسندگان
چکیده
We use a theorem by Ding, Lubetzky and Peres describing the structure of the giant component of random graphs in the strictly supercritical regime, in order to determine the typical size of MAXCUT of G ∼ G (
منابع مشابه
An Upper Bound for the Maximum Cut Mean Value
Let MaxCut(G) be the value of the maximum cut of a graph G. Let f(x, n) be the expectation of MaxCut(G)/xn for random graphs with n vertices and xn edges and let r(x, n) be the expectation of MaxCut(G)/xn for random 2x-regular graphs with n vertices. We prove, for sufficiently large x: 1. limn→∞ f(x, n) ≤ 12 + √ ln 2 2x , 2. limn→∞ r(x, n) ≤ 12 + 1 √ x + 1 2 ln x x .
متن کاملColoring Random and Semi-Random k-Colorable Graphs
The problem of coloring a graph with the minimum number of colors is well known to be NPhard, even restricted to k-colorable graphs for constant k 3. On the other hand, it is known that random k-colorable graphs are easy to k-color. The algorithms for coloring random kcolorable graphs require fairly high edge densities, however. In this paper we present algorithms that color randomly generated ...
متن کاملMinimum Coloring Random and Semi-Random Graphs in Polynomial Expected Time
We present new algorithms for k-coloring and minimum (x(G)-) coloring random and semi-random kcolorable graphs in polynomial expected time. The random graphs are drawn from the G(n,p, k) model and the semi-random graphs are drawn from the G s ~ ( n , p , k) model. In both models, an adversary initially splits the n vertices into IC color classes, each of size @(n). Then the edges between vertic...
متن کاملThe distant-2 chromatic number of random proximity and random geometric graphs
We are interested in finding bounds for the distant-2 chromatic number of geometric graphs drawn from different models. We consider two undirected models of random graphs: random geometric graphs and random proximity graphs for which sharp connectivity thresholds have been shown. We are interested in a.a.s. connected graphs close just above the connectivity threshold. For such subfamilies of ra...
متن کاملAsymptotic behaviour of the complexity of coloring sparse random graphs∗
The behaviour of a backtrack algorithm for graph coloring is well understood for large random graphs with constant edge density. However, sparse graphs, in which the edge density decreases with increasing graph size, are more common in practice. Therefore, in this paper we analyze the expected runtime of a usual backtrack search to color such random graphs, when the size of the graph tends to i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1603.04044 شماره
صفحات -
تاریخ انتشار 2016