منابع مشابه
Embedding Spanning Trees in Random Graphs
We prove that if T is a tree on n vertices with maximum degree ∆ and the edge probability p(n) satisfies: np ≥ C max{∆ log n, n } for some constant > 0, then with high probability the random graph G(n, p) contains a copy of T . The obtained bound on the edge probability is shown to be essentially tight for ∆ = n.
متن کاملLocal resilience of almost spanning trees in random graphs
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically almost surely contains a copy of every tree with maximum degree at most D and at most (1− α)n vertices, even after we delete a (1/2− γ)-fraction of the edges incident to each vertex. The proof uses Szemerédi’s regularity lem...
متن کاملMinimum congestion spanning trees in bipartite and random graphs
The first problem considered in this paper: is it possible to find upper estimates for the spanning tree congestion for bipartite graphs which are better than for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n 3 2 , where n is the number of vertices. The second problem is to estimate spanning tree congestion of rand...
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
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: SIAM Journal on Discrete Mathematics
سال: 2010
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100805753