منابع مشابه
Linked partitions and linked cycles
The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [n+1] is equal to the n-th large Schröder number rn, which counts the number of Schröder paths. In this paper we give a bijective proof of this result. Then we introduce the structures of linked partitions and linked cy...
متن کاملRandom partitions and edge-disjoint Hamiltonian cycles
Nash-Williams [21] proved that every graph with n vertices and minimum degree n/2 has at least b5n/224c edge-disjoint Hamiltonian cycles. In [20], he raised the question of determining the maximum number of edge-disjoint Hamiltonian cycles, showing an upper bound of b(n+ 4)/8c. Let α(δ, n) = (δ + √ 2δn− n2)/2. Christofides, Kühn, and Osthus [7] proved that for every > 0, every graph G on a suff...
متن کاملUniversal and Near-Universal Cycles of Set Partitions
We study universal cycles of the set P(n, k) of k-partitions of the set [n] := {1, 2, . . . , n} and prove that the transition digraph associated with P(n, k) is Eulerian. But this does not imply that universal cycles (or ucycles) exist, since vertices represent equivalence classes of partitions. We use this result to prove, however, that ucycles of P(n, k) exist for all n > 3 when k = 2. We re...
متن کاملk-Efficient partitions of graphs
A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کاملMaximum cuts and judicious partitions in graphs without short cycles
We consider the bipartite cut and the judicious partition problems in graphs of girth at least 4. For the bipartite cut problem we show that every graph G with m edges, whose shortest cycle has length at least rX4; has a bipartite subgraph with at least m 2 þ cðrÞm r rþ1 edges. The order of the error term in this result is shown to be optimal for r 1⁄4 5 thus settling a special case of a conjec...
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: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.2307/2043873