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1.
We represent a graph by assigning each vertex a finite set such that vertices are adjacent if and only if the corresponding sets have at least two common elements. The 2-intersection number θ2(G) of a graph G is the minimum size of the union of sets in such a representation. We prove that the maximum order of a path that can be represented in this way using t elements is between (t2 - 19t + 4)/4 and (t2 - t + 6)/4, making θ2(Pn) asymptotic to 2√n. We also show the existence of a constant c depending on ? such that, for any tree T with maximum degree at most d, θ2(T) ≤ c(√n)1+?. When the maximum degree is not bounded, there is an n-vertex tree T with θ2(T) > .945n2/3. © 1995 John Wiley & Sons, Inc. 相似文献
2.
Boris Pittel 《Random Structures and Algorithms》1990,1(3):311-342
For each of the two models of a sparse random graph on n vertices, G(n, # of edges = cn/2) and G(n, Prob (edge) = c/n) define tn(k) as the total number of tree components of size k (1 ≤ k ≤ n). the random sequence {[tn(k) - nh(k)]n?1/2} is shown to be Gaussian in the limit n →∞, with h(k) = kk?2ck?1e?kc/k! and covariance function being dependent upon the model. This general result implies, in particular, that, for c> 1, the size of the giant component is asymptotically Gaussian, with mean nθ(c) and variance n(1 ? T)?2(1 ? 2Tθ)θ(1 ? θ) for the first model and n(1 ? T)?2θ(1 ? θ) for the second model. Here Te?T = ce?c, T<1, and θ = 1 ? T/c. A close technique allows us to prove that, for c < 1, the independence number of G(n, p = c/n) is asymptotically Gaussian with mean nc?1(β + β2/2) and variance n[c?1(β + β2/2) ?c?2(c + 1)β2], where βeβ = c. It is also proven that almost surely the giant component consists of a giant two-connected core of size about n(1 ? T)β and a “mantle” of trees, and possibly few small unicyclic graphs, each sprouting from its own vertex of the core. 相似文献
3.
《Quaestiones Mathematicae》2013,36(3-4):235-245
Abstract Let G be a graph and let v be a vertex of G. The open neigbourhood N(v) of v is the set of all vertices adjacent with v in G. An open packing of G is a set of vertices whose open neighbourhoods are pairwise disjoint. The lower open packing number of G, denoted ρ° L(G), is the minimum cardinality of a maximal open packing of G while the (upper) open packing number of G, denoted ρ°(G), is the maximum cardinality among all open packings of G. It is known (see [7]) that if G is a connected graph of order n ≥3, then ρ°(G) ≤ 2n/3 and this bound is sharp (even for trees). As a consequence of this result, we know that ρ° L(G) ≤ 2n/3. In this paper, we improve this bound when G is a tree. We show that if G is a tree of order n with radius 3, then ρ° L(G) ≤ n/2 + 2 √n-1, and this bound is sharp, while if G is a tree of order n with radius at least 4, then ρ° L(G) is bounded above by 2n/3—O√n). 相似文献
4.
Jaume Martí-Farré 《代数通讯》2013,41(4):1567-1577
Let I be an ideal of a Noetherian ring R and let S be a multiplicatively closed subset of R. We define the n-th (S)-symbolic power of 7 as S(In) = InRs ∩R. The purpose of this paper is to compare the topologies defined by the adic {In}n≤0 and the (S)-symbolic filtration {S(In)}n≥o using the direct system {Exti R(R/In,R)}n≥0 相似文献
5.
A. G. Ramm 《Mathematical Methods in the Applied Sciences》1992,15(3):159-166
The Radon transform R(p, θ), θ∈Sn?1, p∈?1, of a compactly supported function f(x) with support in a ball Ba of radius a centred at the origin is given for all $ \theta \in \mathop {S^{n - 1} }\limits^\tilde $, where $ \mathop {S^{n - 1} }\limits^\tilde $ is an open set on Sn?1, and all p∈(? ∞, ∞), n≥2. An approximate formula is given to calculate f(x) from the given data. 相似文献
6.
For the maximum number f(n) of edges in a C4-free subgraph of the n-dimensional cube-graph Qn we prove f(n) ≥ 1/2(n +√n)2n?1 for n = 4r, and f(n) ≥ 1/2(n +0.9√n)2n?1 for all n ≥ 9. This disproves one version of a conjecture of P. Erdos. © 1995 John Wiley & Sons, Inc. 相似文献
7.
Klaus Pinn 《Complexity》1999,4(3):41-46
A number of observations are made on Hofstadter's integer sequence defined by Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n − 2)), for n > 2, and Q(1) = Q(2) = 1. On short scales, the sequence looks chaotic. It turns out, however, that the Q(n) can be grouped into a sequence of generations. The k‐th generation has 2k members that have “parents” mostly in generation k − 1 and a few from generation k − 2. In this sense, the sequence becomes Fibonacci type on a logarithmic scale. The variance of S(n) = Q(n) − n/2, averaged over generations, is ≅2αk, with exponent α = 0.88(1). The probability distribution p*(x) of x = R(n) = S(n)/nα, n ≫ 1, is well defined and strongly non‐Gaussian, with tails well described by the error function erfc. The probability distribution of xm = R(n) − R(n − m) is given by pm(xm) = λm p*(xm/λm), with λm → √2 for large m. © 1999 John Wiley & Sons, Inc. 相似文献
8.
An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exists an equitable coloring of a graph G with k colors is said to be the equitable chromatic number of G and is denoted by χ=(G). The least positive integer k such that for any k′ ≥ k there exists an equitable coloring of a graph G with k′ colors is said to be the equitable chromatic threshold of G and is denoted by χ=*(G). In this paper, we investigate the asymptotic behavior of these coloring parameters in the probability space G(n,p) of random graphs. We prove that if n?1/5+? < p < 0.99 for some 0 < ?, then almost surely χ(G(n,p)) ≤ χ=(G(n,p)) = (1 + o(1))χ(G(n,p)) holds (where χ(G(n,p)) is the ordinary chromatic number of G(n,p)). We also show that there exists a constant C such that if C/n < p < 0.99, then almost surely χ(G(n,p)) ≤ χ=(G(n,p)) ≤ (2 + o(1))χ(G(n,p)). Concerning the equitable chromatic threshold, we prove that if n?(1??) < p < 0.99 for some 0 < ?, then almost surely χ(G(n,p)) ≤ χ=* (G(n,p)) ≤ (2 + o(1))χ(G(n,p)) holds, and if < p < 0.99 for some 0 < ?, then almost surely we have χ(G(n,p)) ≤ χ=*(G(n,p)) = O?(χ(G(n,p))). © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009 相似文献
9.
We determine all S(3, κ, 17)'s which either; (i) have a block of size at least 6; or (ii) have an automorphism group order divisible by 17, 5, or 3; or (iii) contain a semi-biplane; or (iv) come from an S(3, κ, 16) which is not an S(3, 4, 16). There is an S(3, κ, 17) with |G| = n if and only if n ϵ {2a3b: 0 ≤ a ≤ 7,0 ≤ b ≤ 1} ∪ {18, 60, 144, 288, 320, 1920, 5760, 16320}. We also search the S(3, κ, 17)'s listed in the appendix for subdesigns S(2, κ, 17) and generate 22 nonisomorphic S(3, κ, 18)'s by adding a new point to such a subdesign. © 1997 John Wiley & Sons, Inc. 相似文献
10.
M. Lashkarizadeh Bami 《Semigroup Forum》2004,69(2):219-229
In the present paper it is shown that if S1 and S2 are two
Clifford topological semigroups satisfying certain conditions
and T is an isometric isomorphism of LUC(S1*) onto LUC(S2*), then T
maps S1 topologically isomorphically onto S2. Furthermore, T
maps M
l
n(S1) (M(S1), respectively) isometrically
isomorphically onto M
l
n(S2) (M(S2), respectively). Indeed,
we have obtained a generalization of a well-known result of
Ghahramani, Lau and Losert for locally compact groups to a more
general setting of Clifford topological semigroups. 相似文献
11.
In this work we introduce the concept of n
–1-isomorphism between Steiner systems (this coincides with the concept of isomorphism whenever n=1).Precisely two Steiner systems S1
and S2
are said to be n–1-isomorphic if there exist n partial systems S
i
(1)
,...,S
i
(n)
contained in Si, i.{1,2},such that S
1
(k)
and S
2
(k)
are isomorphic for each k{1,..., n}.The n–1-isomorphisms are also used to study nets replacements, see Ostrom [8], and to study the transformation methods of designs and other incidence structures introduced in [9] and generalized in [1] and [10].Work done under the auspicies of G.N.S.A.G.A. supported by 40% grants of M.U.R.S.T. 相似文献
12.
Sunto Si studiano i sottogruppi abeliani diSp(n)·Sp(1). Viene data una caratterizzazione dei sottogruppi abeliani G diSp(n)·Sp(1) che sono immagini di sottogruppi abeliani del rivestimento universaleSp(n)·Sp(1). In relazione all'azione diSp(n)·Sp(1) su R4n ≡ Qn si determinano i sottogruppi abeliani G per i quali Qn si decompone nella somma diretta di di n sottospazi quaternionali1-dimensionali invarianti per G. Si caratterizzano i sottogruppi abeliani massimali tra quelli del tipo Zp × … × Zp (p numero primo).
Entrata in Redazione il 21 Luglio 1976. 相似文献
13.
A. D. Korshunov 《Mathematical Notes》1971,9(3):155-160
LetG(n) be the set of all nonoriented graphs with n enumerated points without loops or multiple lines, and let vk(G) be the number of mutually nonisomorphic k-point subgraphs of G G(n). It is proved that at least |G(n)| (1–1/n) graphs G G(n) possess the following properties: a) for any k [6log2n], where c=–c log2c–(1–c)×log2(1–c) and c>1/2, we havev
k(G) > C
n
k
(1–1/n2); b) for any k [cn + 5 log2n] we havev
k(G) = C
n
k
. Hence almost all graphs G G(n) containv(G) 2n pairwise nonisomorphic subgraphs.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 263–273, March, 1971. 相似文献
14.
E. Gečiauskas 《Geometriae Dedicata》2006,121(1):9-18
We have obtained a recurrence formula $I_{n+3} = \frac{4(n+3)}{\pi(n+4)}VI_{n+1}We have obtained a recurrence formula
In+3 = \frac4(n+3)p(n+4)VIn+1I_{n+3} = \frac{4(n+3)}{\pi(n+4)}VI_{n+1} for integro-geometric moments in the case of a circle with the area V, where
In = ò\nolimitsK ?Gsnd GI_n = \int \nolimits_{K \cap G}\sigma^{n}{\rm d} G, while in the case of a convex domain K with the perimeter S and area V the recurrence formula
In+3 = \frac8(n+3)V2(n+1)(n+4)p[\fracd In+1d V - \fracIn+1S \fracd Sd V ] I_{n+3} = \frac{8(n+3)V^2}{(n+1)(n+4)\pi}\Big[\frac{{\rm d} I_{n+1}}{{\rm d} V} - \frac{I_{n+1}}{S} \frac{{\rm d} S}{{\rm d} V} \Big] 相似文献
15.
Let n = (p − 1) · p
k
, where p is a prime number such that 2 is a primitive root modulo p, and 2
p−1 − 1 is not a multiple of p
2. For a standard basis of the field GF(2
n
), a multiplier of complexity O(log log p)n log n log log
p
n and an inverter of complexity O(log p log log p)n log n log log
p
n are constructed. In particular, in the case p = 3 the upper bound
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