共查询到20条相似文献,搜索用时 640 毫秒
1.
Mirko Horňák 《Discrete Mathematics》2008,308(7):1268-1281
A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ; from a result by Barth and Fournier it follows that Δ(T)?4. A necessary and a sufficient condition for being an arbitrarily vertex decomposable star-like tree have been exhibited. The conditions seem to be very close to each other. 相似文献
2.
Rafa? Kalinowski Monika Pil?niak Mariusz Wo?niak Irmina Zio?o 《Discrete Mathematics》2009,309(11):3726-3732
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1,…,nk) of positive integers with n1+?+nk=n, there exists a partition (V1,…,Vk) of the vertex set of G such that Vi induces a connected subgraph of order ni, for all i=1,…,k. A sun with r rays is a unicyclic graph obtained by adding r hanging edges to r distinct vertices of a cycle. We characterize all arbitrarily vertex decomposable suns with at most three rays. We also provide a list of all on-line arbitrarily vertex decomposable suns with any number of rays. 相似文献
3.
Mirko Horňák Antoni Marczyk Ingo Schiermeyer Mariusz Wo?niak 《Graphs and Combinatorics》2012,28(6):807-821
A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n 1, . . . , n k ) of positive integers such that n 1 + · · · + n k = n there exists a partition (V 1, . . . , V k ) of the vertex set of G such that for each ${i \in \{1,\ldots,k\}}$ , V i induces a connected subgraph of G on n i vertices. The main result of the paper reads as follows. Suppose that G is a connected graph on n ≥ 20 vertices that admits a perfect matching or a matching omitting exactly one vertex. If the degree sum of any pair of nonadjacent vertices is at least n ? 5, then G is arbitrarily vertex decomposable. We also describe 2-connected arbitrarily vertex decomposable graphs that satisfy a similar degree sum condition. 相似文献
4.
We give a complete characterization of on-line arbitrarily vertex decomposable graphs in the family of unicycle graphs called suns. A sun is a graph with maximum degree three, such that deleting vertices of degree one results in a cycle. This result has already been used in another paper to prove some Ore-type conditions for on-line arbitrarily decomposable graphs. 相似文献
5.
Antoni Marczyk 《Discrete Mathematics》2009,309(11):3588-3594
Let G be a graph of order n and r, 1≤r≤n, a fixed integer. G is said to be r-vertex decomposable if for each sequence (n1,…,nr) of positive integers such that n1+?+nr=n there exists a partition (V1,…,Vr) of the vertex set of G such that for each i∈{1,…,r}, Vi induces a connected subgraph of G on ni vertices. G is called arbitrarily vertex decomposable if it is r-vertex decomposable for each r∈{1,…,n}.In this paper we show that if G is a connected graph on n vertices with the independence number at most ⌈n/2⌉ and such that the degree sum of any pair of non-adjacent vertices is at least n−3, then G is arbitrarily vertex decomposable or isomorphic to one of two exceptional graphs. We also exhibit the integers r for which the graphs verifying the above degree-sum condition are not r-vertex decomposable. 相似文献
6.
Dominique Barth 《Discrete Mathematics》2006,306(5):469-477
A n-vertex graph is said to be decomposable if for any partition (λ1,…,λp) of the integer n, there exists a sequence (V1,…,Vp) of connected vertex-disjoint subgraphs with |Vi|=λi. In this paper, we focus on decomposable trees. We show that a decomposable tree has degree at most 4. Moreover, each degree-4 vertex of a decomposable tree is adjacent to a leaf. This leads to a polynomial time algorithm to decide if a multipode (a tree with only one vertex of degree greater than 2) is decomposable. We also exhibit two families of decomposable trees: arbitrary large trees with one vertex of degree 4, and trees with an arbitrary number of degree-3 vertices. 相似文献
7.
Ming-Huat Lim 《Linear algebra and its applications》2008,428(1):239-253
Let T be an additive mapping from a tensor product of vector spaces over a field into itself. We describe T for the following two cases: (i) T is surjective and sends non-zero decomposable elements to non-zero decomposable elements, and (ii) T(A) is a non-zero decomposable element if and only if A is a non-zero decomposable element. 相似文献
8.
Turdebek N. Bekjan 《Journal of Functional Analysis》2008,254(9):2401-2418
Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L2(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations. 相似文献
9.
Ridgley Lange 《Journal of Mathematical Analysis and Applications》1975,49(3):721-724
The author shows that, for an injective analytic function f, f(T) is almost decomposable iff T is almost decomposable, where T is a bounded linear operator on a Banach space and f(T) is defined by the functional calculus. 相似文献
10.
For n ≥ 3, the complete n‐vertex multidigraph with any fixed multiplicity of edges is proved to be decomposable into nonhamiltonian (directed) paths of arbitrarily prescribed lengths (≤ n ? 2) provided that the lengths sum up to the size of the multidigraph. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献
11.
A n-vertex graph is said to be decomposable if, for any partition (λ1,…,λp) of the integer n, there exists a sequence (V1,…,Vp) of connected vertex-disjoint subgraphs with |Vi|=λi. The aim of the paper is to study the homeomorphism classes of decomposable trees. More precisely, we show that homeomorphism classes containing decomposable trees with an arbitrarily large minimal distance between all pairs of distinct vertices of degree different from 2, is exactly the set of combs. 相似文献
12.
In this paper, we continue our spectral-theoretic study [8] of unbounded closed operators in the framework of the spectral decomposition property and decomposable operators. Given a closed operator T with nonempty resolvent set, let f → f(T) be the homomorphism of the functional calculus. We show that if T has the spectral decomposition property, then f(T) is decomposable. Conversely, if f is nonconstant on every component of its domain which intersects the spectrum of T, then f(T) decomposable implies that T has the spectral decomposition property. A spectral duality theorems follows as a corollary. Furthermore, we obtain an analytic-type property for the canonical embedding J of the underlying Banach space X into its second dual . 相似文献
13.
Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t
1,..., t
p
) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T
1,..., t
p
) of pairwise edge-disjoint closed trails in G such that T
i
is of length T
i
for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and M
a,a
is a perfect matching in K
a,a
, then the graph K
a,a
-M
a,a
is arbitrarily decomposable into closed trails.
相似文献
14.
Qualitative properties of solutions in the time differential dual-phase-lag model of heat conduction
In this paper we study the time differential dual-phase-lag model of heat conduction incorporating the microstructural interaction effect in the fast-transient process of heat transport. We analyze the influence of the delay times upon some qualitative properties of the solutions of the initial boundary value problems associated to such a model. Thus, the uniqueness results are established under the assumption that the conductivity tensor is positive definite and the delay times τq and τT vary in the set {0 ≤ τq ≤ 2τT} ∪ {0 < 2τT < τq}. For the continuous dependence problem we establish two different estimates. The first one is obtained for the delay times with 0 ≤ τq ≤ 2τT, which agrees with the thermodynamic restrictions on the model in concern, and the solutions are stable. The second estimate is established for the delay times with 0 < 2τT < τq and it allows the solutions to have an exponential growth in time. The spatial behavior of the transient solutions and the steady-state vibrations is also addressed. For the transient solutions we establish a theorem of influence domain, under the assumption that the delay times are in {0 < τq ≤ 2τT} ∪ {0 < 2τT < τq}. While for the amplitude of the harmonic vibrations we obtain an exponential decay estimate of Saint–Venant type, provided the frequency of vibration is lower than a critical value and without any restrictions upon the delay times. 相似文献
15.
Günter M. Ziegler 《Israel Journal of Mathematics》1994,87(1-3):97-110
16.
Richard Moynihan 《Journal of Mathematical Analysis and Applications》1980,74(1):15-30
This paper introduces the use of conjugate transforms in the study of τT semigroups of probability distribution functions. If Δ+ denotes the space of one-dimensional distribution functions concentrated on [0, ∞) and T is a t-norm, i.e., a suitable binary operation on [0, 1], then the operation τT is defined for F, G in Δ+by τT(F, G)(x) = supu+v = xT(F(u), G(v)) for all x. The pair (Δ+, τT) is then a semigroup. For any Archimedean t-norm T, a conjugate transform CT is defined on (Δ+, τT). These transforms are shown to play a role similar to that played by the Laplace transform on the convolution semigroup. Thus a theory of “characteristic functions” for τT semigroups is developed. In addition to establishing their basic algebraic properties, we also use conjugate transforms to study the algebraic questions of the cancellation law, infinitely divisible elements, and solutions of equations in τT semigroups. 相似文献
17.
In τ-tilting theory, it is often difficult to determine when a set of bricks forms a 2-simple minded collection. The aim of this paper is to determine when a set of bricks is contained in a 2-simple minded collection for a τ-tilting finite algebra. We begin by extending the definition of mutation from 2-simple minded collections to more general sets of bricks (which we call semibrick pairs). This gives us an algorithm to check if a semibrick pair is contained in a 2-simple minded collection. We then use this algorithm to show that the 2-simple minded collections of a τ-tilting finite gentle algebra (whose quiver contains no loops or 2-cycles) are given by pairwise compatibility conditions if and only if every vertex in the corresponding quiver has degree at most 2. As an application, we show that the classifying space of the τ-cluster morphism category of a τ-tilting finite gentle algebra (whose quiver contains no loops or 2-cycles) is an Eilenberg-MacLane space if every vertex in the corresponding quiver has degree at most 2. 相似文献
18.
Gábor Lukács 《Topology and its Applications》2006,153(15):2922-2932
A sequence {an} in a group G is a T-sequence if there is a Hausdorff group topology τ on G such that . In this paper, we provide several sufficient conditions for a sequence in an abelian group to be a T-sequence, and investigate special sequences in the Prüfer groups Z(p∞). We show that for p≠2, there is a Hausdorff group topology τ on Z(p∞) that is determined by a T-sequence, which is close to being maximally almost-periodic—in other words, the von Neumann radical n(Z(p∞),τ) is a non-trivial finite subgroup. In particular, n(n(Z(p∞),τ))?n(Z(p∞),τ). We also prove that the direct sum of any infinite family of finite abelian groups admits a group topology determined by a T-sequence with non-trivial finite von Neumann radical. 相似文献
19.
Edward S. Letzter 《Israel Journal of Mathematics》2012,192(1):67-81
We study prime ideals in skew power series rings T:= R[[y; τ, δ]], for suitably conditioned complete right Noetherian rings R, automorphisms τ of R, and τ-derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim of T, we prove: If I is an ideal of R, then there exists a τ-prime ideal P of T contracting to I if and only if I is a τ-δ-prime ideal of R. Consequently, under the more specialized assumption that δ = τ ? id (a basic feature of the Iwasawa-theoretic context), we can conclude: If I is an ideal of R, then there exists a prime ideal P of T contracting to I if and only if I is a τ-prime ideal of R. Our approach depends essentially on two key ingredients: First, the algebras considered are Zariskian (in the sense of Li and Van Oystaeyen), and so the ideals are all topologically closed. Second, topological arguments can be used to apply previous results of Goodearl and the author on skew polynomial rings. 相似文献
20.
We show that in the constructible universe, the two usual definitions of Butler groups are equivalent for groups of arbitrarily
large power. We also prove that Bext2(G, T) vanishes for every torsion-free groupG and torsion groupT. Furthermore, balanced subgroups of completely decomposable groups are Butler groups. These results have been known, under
CH, only for groups of cardinalities ≤ ℵω.
Partial support by NSF is gratefully acknowledged.
Partially supported by U.S.-Israel Binational Science Foundation. 相似文献