Asymptotically Optimal Tree-Packings in Regular Graphs
نویسندگان
چکیده
Let T be a tree with t vertices. Clearly, an n vertex graph contains at most n/t vertex disjoint trees isomorphic to T . In this paper we show that for every > 0, there exists a D( , t) > 0 such that, if d > D( , t) and G is a simple d-regular graph on n vertices, then G contains at least (1− )n/t vertex disjoint trees isomorphic to T .
منابع مشابه
Local algorithms for independent sets are half-optimal
We show that the largest density of factor of i.i.d. independent sets on the d-regular tree is asymptotically at most (log d)/d as d → ∞. This matches the lower bound given by previous constructions. It follows that the largest independent sets given by local algorithms on random dregular graphs have the same asymptotic density. In contrast, the density of the largest independent sets on these ...
متن کاملOptimal Cycle Codes Constructed From Ramanujan Graphs
We aim here at showing how some known Ramanujan Cayley graphs yield error-correcting codes that are asymptotically optimal in the class of cycle codes of graphs. The main reason why known constructions of Ramanujan graphs yield good cycle codes is that the number of their cycles of a given length behaves essentially like that of random regular graphs. More precisely we show that for actual cons...
متن کاملOptimal Packings of Hamilton Cycles in Sparse Random Graphs
We prove that there exists a positive constant ε such that if log n/n ≤ p ≤ n−1+ε, then asymptotically almost surely the random graph G ∼ G(n, p) contains a collection of bδ(G)/2c edge-disjoint Hamilton cycles.
متن کاملOn spanning tree packings of highly edge connected graphs
We prove a refinement of the tree packing theorem by Tutte/Nash-Williams for finite graphs. This result is used to obtain a similar result for end faithful spanning tree packings in certain infinite graphs and consequently to establish a sufficient Hamiltonicity condition for the line graphs of such graphs.
متن کاملAny Load-Balancing Regimen for Evolving Tree Computations on Circulant Graphs Is Asymptotically Optimal
We analyze evolving tree computations on circulant (rings with “regular” chords) and related graphs. In an evolving α-ary tree computation, a complete tree grows level by level, i. e., every leaf generates α new nodes that become the new leaves. The load balancing task is to spread the new nodes on a network of processors in the moment they were created in such a way that the accumulated number...
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:
- Electr. J. Comb.
دوره 8 شماره
صفحات -
تاریخ انتشار 2001