共查询到20条相似文献,搜索用时 15 毫秒
1.
Knut Deimer 《Combinatorica》1985,5(2):109-120
Ad-dimensional circuit code of spreads is a simple circuitC in the graph of thed-dimen sional unit cube with the property that for any verticesx andy ofC which differ in exactlyr co-ordinates,r<s, there exists a path fromx toy consisting ofr edges ofC. This property is useful for detecting and limiting errors. In this paper we give a new upper bound for the maximum length
of ad-dimensional circuit code of spread 2. 相似文献
2.
A new lower bound for Snake-in-the-Box Codes 总被引:1,自引:0,他引:1
In this paper we give a new lower bound on the length of Snake-in-the-Box Codes, i.e., induced cycles in thed-dmensional cube. The bound is a linear function of the number of vertices of the cube and improves the boundc·2
d
/d, wherec is a constant, proved by Danzer and Klee. 相似文献
3.
Ervin Győri 《Combinatorica》1991,11(3):231-243
In this paper, we prove that any graph ofn vertices andt
r–1(n)+m edges, wheret
r–1(n) is the Turán number, contains (1–o(1)m edge disjointK
r'sifm=o(n
2). Furthermore, we determine the maximumm such that every graph ofn vertices andt
r–1(n)+m edges containsm edge disjointK
r's ifn is sufficiently large.Research partially supported by Hungarian National Foundation for Scientific Research Grant no. 1812. 相似文献
4.
Natural bounded concentrators 总被引:1,自引:0,他引:1
Moshe Morgenstern 《Combinatorica》1995,15(1):111-122
We give the first known direct construction for linear families of bounded concentrators. The construction is explicit and
the results are simple natural bounded concentrators.
Let
be the field withq elements,g(x)∈F
q
[x] of degree greater than or equal to 2,
and
. LetI
nputs=H/A,O
utputs=H/B, and draw an edge betweenaA andbB iffaA∩bB≠ϕ. We prove that for everyq≥5 this graph is an
concentrator.
Part of this research was done while the author was at the department of Computer Science, The University of British Columbia,
Vancouver, B.C., Canada. 相似文献
5.
Peter Dukes 《Discrete Mathematics》2008,308(18):4272-4275
A family F of k-subsets of an n-set X is disjoint union-free (DUF) if all disjoint pairs of elements of F have distinct unions; that is, if for every A,B,C,D∈F, A∩B=C∩D=∅ and A∪B=C∪D implies {A,B}={C,D}. DUF families of maximum size have been studied by Erdös and Füredi. Let F be DUF with the property that F∪{E} is not DUF for any k-subset E of X not already in F. Then F is maximally DUF. We introduce the problem of finding the minimum size of maximally DUF families and provide bounds on this quantity for k=3. 相似文献
6.
Guoli Ding 《Combinatorica》1996,16(3):331-341
Letc(G) denote the number of circuits of a graphG. In this paper, we characterize those minor-closed classesG of graphs for which there is a polynomial functionp(.) such thatc(G)p(|E(G)|) for all graphsG inG. 相似文献
7.
Guoli Ding 《Combinatorica》1995,15(2):159-165
Letb(M) andc(M), respectively, be the number of bases and circuits of a matroidM. For any given minor closed class? of matroids, the following two questions, are investigated in this paper. (1) When is there a polynomial functionp(x) such thatb(M)≤p(c(m)|E(M)|) for every matroidM in?? (2) When is there a polynomial functionp(x) such thatb(M)≤p(|E(M)|) for every matroidM in?? Let us denote byM Mn the direct sum ofn copies ofU 1,2. We prove that the answer to the first question is affirmative if and only if someM Mn is not in?. Furthermore, if all the members of? are representable over a fixed finite field, then we prove that the answer to the second question is affirmative if and only if, also, someM Mn is not in?. 相似文献
8.
The transversal number, packing number, covering number and strong stability number of hypergraphs are denoted by τ, ν, ϱ
and α, respectively. A hypergraph family t is called τ-bound (ϱ-bound) if there exists a “binding function”f(x) such that τ(H)≦f(v(H)) (ϱ(H)≦f(α(H))) for allH ∈ t. Methods are presented to show that various hypergraph families are τ-bound and/or ϱ-bound. The results can be applied
to families of geometrical nature like subforests of trees, boxes, boxes of polyominoes or to families defined by hypergraph
theoretic terms like the family where every subhypergraph has the Helly-property. 相似文献
9.
The energy of a graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. Let T(n,γ) be the set of trees of order n and with domination number γ. In this paper, we characterize the tree from T(n,γ) with the minimal energy, and determine the tree from T(n,γ) where n=kγ with maximal energy for . 相似文献
10.
János Komlós 《Combinatorica》1997,17(3):393-400
We estimate the number of vertices/edges necessary to cover all odd cycles in graphs of given order and odd girth.To the memory of Pál Erds 相似文献
11.
G. A. Margulis 《Combinatorica》1982,2(1):71-78
We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to low density codes is given. 相似文献
12.
Rolando Magnanini Shigeru Sakaguchi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
We consider nonlinear diffusion of some substance in a container (not necessarily bounded) with bounded boundary of class C2. Suppose that, initially, the container is empty and, at all times, the substance at its boundary is kept at density 1. We show that, if the container contains a proper C2-subdomain on whose boundary the substance has constant density at each given time, then the boundary of the container must be a sphere. We also consider nonlinear diffusion in the whole RN of some substance whose density is initially a characteristic function of the complement of a domain with bounded C2 boundary, and obtain similar results. These results are also extended to the heat flow in the sphere SN and the hyperbolic space HN. 相似文献
13.
In this paper we consider boundary-value problems in domains with perforated boundaries. We use the classification of homogenized (limit) problems depending on the ratio of small parameters, which characterize the diameter of the holes and the distance between them. We study the analogue of the Helmholtz resonator for domains with a perforated boundary. 相似文献
14.
For z1,z2,z3∈Zn, the tristance d3(z1,z2,z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticodeAd of diameter d is a subset of Zn with the property that d3(z1,z2,z3)?d for all z1,z2,z3∈Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z2 for all diameters d?1. We then generalize this result to two related distance models: a different distance structure on Z2 where d(z1,z2)=1 if z1,z2 are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z2 is replaced by the hexagonal lattice A2. We also investigate optimal tristance anticodes in Z3 and optimal quadristance anticodes in Z2, and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multi-dimensional interleaving schemes and to connectivity loci in the game of Go. 相似文献
15.
Zoltán Füredi 《Combinatorica》1984,4(2-3):161-168
Let ℓ be a set-system ofr-element subsets on ann-element set,r≧3. It is proved that if |ℓ|>3.5
then ℓ contains four distinct membersA, B, C, D such thatA∪B=C∪D andA∩B=C∩D=0. 相似文献
16.
On the full automorphism group of a graph 总被引:11,自引:0,他引:11
C. D. Godsil 《Combinatorica》1981,1(3):243-256
While it is easy to characterize the graphs on which a given transitive permutation groupG acts, it is very difficult to characterize the graphsX with Aut (X)=G. We prove here that for the certain transitive permutation groups a simple necessary condition is also sufficient. As a corollary
we find that, whenG is ap-group with no homomorphism ontoZ
p
wrZ
p
, almost all Cayley graphs ofG have automorphism group isomorphic toG. 相似文献
17.
A set of vectors is k-independent if all its subsets with no more than k elements are linearly independent. We obtain a result concerning the maximal possible cardinality Ind
q
(n, k) of a k-independent set of vectors in the n-dimensional vector space F
q
n
over the finite field F
q
of order q. Namely, we give a necessary and sufficient condition for Ind
q
(n, k) = n + 1. We conclude with some pertinent remarks re applications of our results to codes, graphs and hypercubes.
Supported, in part by grants EP/C000285, NSF-DMS-0439734 and NSF-DMS-0555839. S. B. Damelin thanks the Institute for Mathematics
and Applications for their hospitality. 相似文献
18.
Benoît Perthame Panagiotis E. Souganidis 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
We provide a mathematical analysis for the appearance of motor effects, i.e., the concentration (as Dirac masses) at one side of the domain, for the solution of a Fokker–Planck system with two components, one with an asymmetric potential and diffusion and one with pure diffusion. The system has been proposed as a model for motor proteins moving along molecular filaments. Its components describe the densities of different conformations of proteins. 相似文献
19.
Zoltán Füredi 《Combinatorica》1981,1(2):155-162
Let ℋ be a family ofr-subsets of a finite setX. SetD(ℋ)=
|{E:x∈E∈ℋ}|, (maximum degree). We say that ℋ is intersecting if for anyH,H′ ∈ ℋ we haveH ∩H′ ≠ 0. In this case, obviously,D(ℋ)≧|ℋ|/r. According to a well-known conjectureD(ℋ)≧|ℋ|/(r−1+1/r). We prove a slightly stronger result. Let ℋ be anr-uniform, intersecting hypergraph. Then either it is a projective plane of orderr−1, consequentlyD(ℋ)=|ℋ|/(r−1+1/r), orD(ℋ)≧|ℋ|/(r−1). This is a corollary to a more general theorem on not necessarily intersecting hypergraphs. 相似文献
20.
We state the following conjecture and prove it for the case whereq is a proper prime power:Let A be a nonsingular n by n matrix over the finite field GFqq4, then there exists a vector x in (GFq)n such that both x and Ax have no zero component.Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild grant. 相似文献