منابع مشابه
Random triangle removal
Starting from a complete graph on n vertices, repeatedly delete the edges of a uniformly chosen triangle. This stochastic process terminates once it arrives at a triangle-free graph, and the fundamental question is to estimate the final number of edges (equivalently, the time it takes the process to finish, or how many edge-disjoint triangles are packed via the random greedy algorithm). Bollobá...
متن کاملTriangle factors in random graphs
A triangle factor of a graph G = (V,E) on n = |V | = 3k vertices, is a subgraph of G consisting of k vertex-disjoint triangles. A result by Krivelevich [9] states that a triangle factor exists in the random graph G(n, p), n = 3k, with probability 1− o(1) if p = Ω(n−2/3+1/15). This was further improved by Jeong Han Kim in [7] to p = ω(n−2/3+1/18). In this paper we improve this to p = n−2/3+o(1)....
متن کاملTriangle Factors in Random Graphs
For a graph G = (V; E) on n vertices, where 3 divides n, a triangle factor is a subgraph of G, consisting of n=3 vertex disjoint triangles (complete graphs on three vertices). We discuss the problem of determining the minimal probability p = p(n), for which a random graph G 2 G(n; p) contains almost surely a triangle factor. This problem (in a more general setting) has been studied by Alon and ...
متن کاملOn Random Greedy Triangle Packing
The behaviour of the random greedy algorithm for constructing a maximal packing of edgedisjoint triangles on n points (a maximal partial triple system) is analysed with particular emphasis on the final number of unused edges. It is shown that this number is at most n, “halfway” from the previous best-known upper bound o(n) to the conjectured value n. The more general problem of random greedy pa...
متن کاملRandom Triangle Theory with Geometry and Applications
What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much more. One of the best distributions of random triangles takes all six vertex coordinates as independent standard Gaussians. Six can be reduced to four by transl...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.04.015