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1.
The so-called Kelly conjecture states that every regular tournament on 2k+1 vertices has a decomposition into k-arc-disjoint hamiltonian cycles. In this paper we formulate a generalization of that conjecture, namely we conjecture that every k-arc-strong tournament contains k arc-disjoint spanning strong subdigraphs. We prove several results which support the conjecture:If D = (V, A) is a 2-arc-strong semicomplete digraph then it contains 2 arc-disjoint spanning strong subdigraphs except for one digraph on 4 vertices.Every tournament which has a non-trivial cut (both sides containing at least 2 vertices) with precisely k arcs in one direction contains k arc-disjoint spanning strong subdigraphs. In fact this result holds even for semicomplete digraphs with one exception on 4 vertices.Every k-arc-strong tournament with minimum in- and out-degree at least 37k contains k arc-disjoint spanning subdigraphs H
1, H
2, . . . , H
k
such that each H
i
is strongly connected.The last result implies that if T is a 74k-arc-strong tournament with speci.ed not necessarily distinct vertices u
1, u
2, . . . , u
k
, v
1, v
2, . . . , v
k
then T contains 2k arc-disjoint branchings
where
is an in-branching rooted at the vertex u
i
and
is an out-branching rooted at the vertex v
i
, i=1,2, . . . , k. This solves a conjecture of Bang-Jensen and Gutin [3].We also discuss related problems and conjectures.
相似文献
Anders YeoEmail: |
2.
A theorem of Deza asserts that ifH
1, ...,H
m
ares-sets any pair of which intersects in exactlyd elements and ifm ≧s
2 −s+2, then theH
i
form aΔ-system, i.e.
. In other words, every large equidistant (0, 1)-code of constant weight is trivial. We give a (0, +1, −1) analogue of this
theorem. 相似文献
3.
Suppose that p = (p1, p2, …, pN) and q = (q1, q2, …, qN) are two configurations in
, which are centers of balls B
d
(p
i
, r
i
) and B
d
(q
i
, r
i
) of radius r
i
, for i = 1, …, N. In [9] it was conjectured that if the pairwise distances between ball centers p are contracted in going to the centers q,
then the volume of the union of the balls does not increase. For d = 2 this was proved in [1], and for the case when the centers are contracted continuously for all d in [2]. One extension
of the Kneser-Poulsen conjecture, suggested in [6], was to consider various Boolean expressions in the unions and intersections
of the balls, called flowers, where appropriate pairs of centers are only permitted to increase, and others are only permitted
to decrease. Again under these distance constraints, the volume of the flower was conjectured to change in a monotone way.
Here we show that these generalized Kneser-Poulsen flower conjectures are equivalent to an inequality between certain integrals
of functions (called flower weight functions) over
, where the functions in question are constructed from maximum and minimum operations applied to functions each being radially
symmetric monotone decreasing and integrable.
Research supported in part by NSF Grant No. DMS-0209595. 相似文献
4.
Let
be the 2k-uniform hypergraph obtained by letting P1, . . .,Pr be pairwise disjoint sets of size k and taking as edges all sets Pi∪Pj with i ≠ j. This can be thought of as the ‘k-expansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain
can be obtained by partitioning V = V1 ∪V2 and taking as edges all sets of size 2k that intersect each of V1 and V2 in an odd number of elements. Let
denote a hypergraph on n vertices obtained by this construction that has as many edges as possible. For n sufficiently large we prove a conjecture of Frankl, which states that any hypergraph on n vertices that contains no
has at most as many edges as
.
Sidorenko has given an upper bound of
for the Tur′an density of
for any r, and a construction establishing a matching lower bound when r is of the form 2p+1. In this paper we also show that when r=2p+1, any
-free hypergraph of density
looks approximately like Sidorenko’s construction. On the other hand, when r is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Turán density
of
to
, where c(r) is a constant depending only on r.
The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections
in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear
algebra, the Kruskal–Katona theorem and properties of Krawtchouck polynomials.
* Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship. 相似文献
5.
Under the assumption that μ is a non-doubling measure on ℝ
d
which only satisfies some growth condition, the authors prove that the maximal multilinear Calderón-Zygmund operator is bounded
from (μ) × … × (μ) into L
p
(μ) for any p
1, … p
m
∈ (1, ∞) and p with 1/p = 1/p
1 + … + 1/p
m
, and bounded from (μ) × … × (μ) into weak-
L
p
(μ) if there exists any p
i
= 1. Furthermore, the authors establish a weighted weak-type estimate for the maximal multilinear Calderón-Zygmund operator.
The second (corresponding) author is supported by Tianyuan Fund of China (No. 10626055) and National Natural Science Foundation
of China (No. 10701078). 相似文献
6.
J. B. Shearer 《Combinatorica》1985,5(3):241-245
LetX
1, ...,X
n
be events in a probability space. Let ϱi be the probabilityX
i
occurs. Let ϱ be the probability that none of theX
i
occur. LetG be a graph on [n] so that for 1 ≦i≦n X
i
is independent of ≈X
j
‖(i, j)∉G≈. Letf(d) be the sup of thosex such that if ϱ1, ..., ϱ
n
≦x andG has maximum degree ≦d then ϱ>0. We showf(1)=1/2,f(d)=(d−1)
d−1
d
−d ford≧2. Hence
df(d)=1/e. This answers a question posed by Spencer in [2]. We also find a sharp bound for ϱ in terms of the ϱ
i
andG. 相似文献
7.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
wherea
i
≠0 is integer,i=1,2…,s. In 1979, Schmidt proved that if ∈>0 then there is a large constantC(k,∈) such that fors>C(k,∈) the equationf(X)=0 has a nontrivial, integer solution in σ1, σ2, …, σ3,x
1,x
2, …,x
3 satisfying
Schmidt did not estimate this constantC(k,∈) since it would be extremely large. In this paper, we prove the following result 相似文献
8.
Jin-cheng XIONG Feng TAN & Jie Lü School of Mathematical Sciences South China Normal University Guangzhou China 《中国科学A辑(英文版)》2007,50(4):475-484
For a probability space (X, B,μ) a subfamily F of theσ-algebra B is said to be a regular base if every B∈B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. Assume that {γr}γ∈Γis a countable family of relations of the full measure on a probability space (X,B,μ), i.e. for everyγ∈Γthere is a positive integer sγsuch that Rγ(?)Xsγwithμsγ(Rγ) = 1. In the present paper we show that if (X, B,μ) has a regular base, the cardinality of which is not greater than the cardinality of the continuum, then there exists a set K(?)X withμ*(K) = 1 such that (x1,...,xsγ)∈γr for anyγ∈Γand for any sγdistinct elements x1,..., xsγof K, whereμ* is the outer measure induced by the measureμ. Moreover, an application of the result mentioned above is given to the dynamical systems determined by the iterates of measure-preserving transformations. 相似文献
9.
Let E be a Galois extension of ℚ of degree l, not necessarily solvable. In this paper we first prove that the L-function L(s, π) attached to an automorphic cuspidal representation π of cannot be factored nontrivially into a product of L-functions over E.
Next, we compare the n-level correlation of normalized nontrivial zeros of L(s, π1)…L(s, π
k
), where π
j
, j = 1,…, k, are automorphic cuspidal representations of , with that of L(s,π). We prove a necessary condition for L(s, π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific , j = 1,…,k. In particular, if π is not invariant under the action of any nontrivial σ ∈ Gal
E/ℚ, then L(s, π) must equal a single L-function attached to a cuspidal representation of and π has an automorphic induction, provided L(s, π) can factored into a product of L-functions over ℚ. As E is not assumed to be solvable over ℚ, our results are beyond the scope of the current theory of base change and automorphic
induction.
Our results are unconditional when m,m
1,…,m
k
are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.
The first author was supported by the National Basic Research Program of China, the National Natural Science Foundation of
China (Grant No. 10531060), and Ministry of Education of China (Grant No. 305009). The second author was supported by the
National Security Agency (Grant No. H98230-06-1-0075). The United States Government is authorized to reproduce and distribute
reprints notwithstanding any copyright notation herein 相似文献
10.
R. V. Hrushevoi 《Ukrainian Mathematical Journal》2008,60(4):540-550
We describe the set
of parameters γ for which there exists a decomposition of the operator γI
H in a sum of n self-adjoint operators with spectra from the sets M
1, …, M
n, M
i = 0, 1, …, k
i, for n ≥ 4 and, in some cases, for n = 3.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 470–477, April, 2008. 相似文献
11.
Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy (i) and (ii) below:
- (i)
- There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal.
- (ii)
- There exists a basis for V with respect to which the matrix representing A∗ is irreducible tridiagonal and the matrix representing A is diagonal.
12.
Markus Brodmann 《manuscripta mathematica》1992,76(1):181-192
Let M be a generalized Cohen-Macaulay module over a noetherian local ring (R,m). Fix a standard system x1, …, xd∈m with respect to M and let
. We construct a coherent Cohen-Macaulay sheafK over the projective space ℙ
R/I
d-1
whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules H
m
i
(M), (i=0, …, d−1). 相似文献
13.
A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd(vi) = Σ(vi,vj)∈E(G) d(vj) holds for all i = 1, 2,..., |V(G)|, where d(vi) denotes the degree of vertex vi. Let ni denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded ni (1 ≤ i ≤ 7) are studied and some interesting results are obtained. 相似文献
14.
Conditions for the existence of a graph with given diameter, connectivity, and ball diversity vector
K. L. Rychkov 《Journal of Applied and Industrial Mathematics》2009,3(1):107-116
Given some arbitrary integers d ≥ 2, ? ? 1 and an integer vector $ \bar \tau Given some arbitrary integers d ≥ 2, ϰ ⩾ 1 and an integer vector
= (τ
0, τ
1, …, τ
d
) with τ
0 ⩾ τ
1 ⩾ … ⩾ τ
d
= 1 and τ
d − 1 ⩾ d
2ϰ + 3, the existence is proved of a graph of diameter d and connectivity ϰ whose ball diversity vector is
. Moreover, the nonexistence is proved of a graph of diameter d with connectivity ϰ and ball diversity vector (τ
0, τ
1, …, τ
d
), where τ
0 < (d − 1)ϰ + 2.
Original Russian Text ? K.L. Rychkov, 2007, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2007, Vol. 14,
No. 4, pp. 43–56. 相似文献
15.
This paper considers thefinitary reconstruction of an ergodic measure preserving transformationT of a complete separable metric spaceX from a single trajectoryx, Tx, …, or more generally, from a suitable reconstruction sequence x=x
1,x
2, … withx
i∈X. Ann-sample reconstruction is a functionT
n: X
n+1 →X; the map
(·;x
1, …,x
n)is treated as an estimate ofT(·) based on then initial elements of x. Given a reference probability measureμ
0 and constantM>1, functionsT
1,T
2, … are defined, and it is shown that for everyμ with 1/M≤dμ/dμ
0≤M, everyμ-preserving transformationT, and every reconstruction sequence x forT, the estimates
(·;x
1, …,x
nconverge toT in the weak topology.
For the family of interval exchange transformations of [0, 1] a simple family of estimates is described and shown to be consistent
both pointwise and in the strong topology. However, it is also shown that no finitary estimation scheme is consistent in the
strong topology for the family of all ergodic Lebesgue measure preserving transformations of the unit interval, even if x
is assumed to be a generic trajectory ofT.
Supported in part by NSF Grant DMS-9501926. 相似文献
16.
If w1,…,w
N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ1,…, λN on the unit circle and positive numbers Μ1,…,Μ
N such that
is the zero sequence of the function 1 —
. The points λ1,…, λN and numbers Μ1,…,ΜN are unique (except for reorderings). 相似文献
17.
A matrixA=(a
ij
) has theEdmonds—Johnson property if, for each choice of integral vectorsd
1,d
2,b
1,b
2, the convex hull of the integral solutions ofd
1≦x≦d
2,b
1≦Ax≦b
2 is obtained by adding the inequalitiescx≦|δ|, wherec is an integral vector andcx≦δ holds for each solution ofd
1≦x≦d
2,b
1≦Ax≦b
2. We characterize the Edmonds—Johnson property for integral matricesA which satisfy
for each (row index)i. A corollary is that ifG is an undirected graph which does not contain any homeomorph ofK
4 in which all triangles ofK
4 have become odd circuits, thenG ist-perfect. This extends results of Boulala, Fonlupt, Sbihi and Uhry.
First author’s research supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). 相似文献
18.
Let K denote a field, and let V denote a vector space over K with finite positive dimension. By a Leonard pair on V we mean an ordered pair of linear transformations A : V → V and A∗ : V → V that satisfy the following two conditions:
- (i)
- There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal.
- (ii)
- There exists a basis for V with respect to which the matrix representing A∗ is irreducible tridiagonal and the matrix representing A is diagonal.
19.
Let Γ be a distance-regular graph of diameter d≥2 and a
1≠0. Let θ be a real number. A pseudo cosine sequence for θ is a sequence of real numbers σ
0,…,σ
d
such that σ
0=1 and c
i
σ
i−1+a
i
σ
i
+b
i
σ
i+1=θ
σ
i
for all i∈{0,…,d−1}. Furthermore, a pseudo primitive idempotent for
θ is E
θ
=s ∑
i=0
d
σ
i
A
i
, where s is any nonzero scalar. Let
be the characteristic vector of a vertex v∈VΓ. For an edge xy of Γ and the characteristic vector w of the set of common neighbours of x and y, we say that the edge xy is tight with respect to
θ whenever θ≠k and a nontrivial linear combination of vectors
,
and Ew is contained in
. When an edge of Γ is tight with respect to two distinct real numbers, a parameterization with d+1 parameters of the members of the intersection array of Γ is given (using the pseudo cosines σ
1,…,σ
d
, and an auxiliary parameter ε).
Let S be the set of all the vertices of Γ that are not at distance d from both vertices x and y that are adjacent. The graph Γ is pseudo 1-homogeneous with respect to
xy whenever the distance partition of S corresponding to the distances from x and y is equitable in the subgraph induced on S. We show Γ is pseudo 1-homogeneous with respect to the edge xy if and only if the edge xy is tight with respect to two distinct real numbers. Finally, let us fix a vertex x of Γ. Then the graph Γ is pseudo 1-homogeneous with respect to any edge xy, and the local graph of x is connected if and only if there is the above parameterization with d+1 parameters σ
1,…,σ
d
,ε and the local graph of x is strongly regular with nontrivial eigenvalues a
1
σ/(1+σ) and (σ
2−1)/(σ−σ
2). 相似文献
20.
By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the
asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation
, on a time scale . The results improve some oscillation results for neutral delay dynamic equations and in the special case when = ℝ our results cover and improve the oscillation results for second-order neutral delay differential equations established
by Li and Liu [Canad. J. Math., 48 (1996), 871–886]. When = ℕ, our results cover and improve the oscillation results for second order neutral delay difference equations established
by Li and Yeh [Comp. Math. Appl., 36 (1998), 123–132]. When =hℕ, = {t: t = q
k
, k ∈ ℕ, q > 1}, = ℕ2 = {t
2: t ∈ ℕ}, = = {t
n
= Σ
k=1
n
, n ∈ ℕ0}, ={t
2: t ∈ ℕ}, = {√n: n ∈ ℕ0} and ={: n ∈ ℕ0} our results are essentially new. Some examples illustrating our main results are given.
相似文献