On disjoint perfect tree-matchings in random graphs
نویسنده
چکیده
For an arbitrary tree T, a T-matching in G is a set of vertex-disjoint subgraphs of G which are isomorphic to T. A T-matching which is a spanning subgraph of G is called a perfect T-matching. For any t-vertex tree T we find a threshold probability function jj = jj( n) for the existence of r edge-disjoint perfect T-matchings in a random graph G(n,p).
منابع مشابه
Perfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملAbstract—alexey Pokrovskiy
Alexey Pokrovskiy Aharoni and Berger conjectured [1] that every bipartite graph which is the union of n matchings of size n + 1 contains a rainbow matching of size n. This conjecture is related to several old conjectures of Ryser, Brualdi, and Stein about transversals in Latin squares. There have been many recent partial results about the Aharoni-Berger Conjecture. When the matchings have size ...
متن کاملThe Number of f-Matchings in Almost Every Tree is a Zero Residue
For graphs F and G an F -matching in G is a subgraph of G consisting of pairwise vertex disjoint copies of F . The number of F -matchings in G is denoted by s(F,G). We show that for every fixed positive integer m and every fixed tree F , the probability that s(F,Tn) ≡ 0 (mod m), where Tn is a random labeled tree with n vertices, tends to one exponentially fast as n grows to infinity. A similar ...
متن کامل0 Trees and Matchings Richard
In this article, Temperley’s bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegative weights that induce a weighting on the set of spanning trees. We show that the weighted, directed spann...
متن کاملMatchings in Random Biregular Bipartite Graphs
We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdős and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.
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:
- Australasian J. Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 1999