共查询到20条相似文献,搜索用时 31 毫秒
1.
Let G be an outerplanar graph with maximum degree △. Let χ(G^2) and A(G) denote the chromatic number of the square and the L(2, 1)-labelling number of G, respectively. In this paper we prove the following results: (1) χ(G^2) = 7 if △= 6; (2) λ(G) ≤ △ +5 if △ ≥ 4, and ),(G)≤ 7 if △ = 3; and (3) there is an outerplanar graph G with △ = 4 such that )λ(G) = 7. These improve some known results on the distance two labelling of outerplanar graphs. 相似文献
2.
The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1(L) = 2λ1 (D), and that for a connected graph G and its line graph L, if one of κ1 (L) and λ(G) exists, then κ1(L) = λ2(G). This paper determines that κ1(B(d, n) is equal to 4d- 8 for n = 2 and d ≥ 4, and to 4d-4 for n ≥ 3 and d ≥ 3, and that κ1(K(d, n)) is equal to 4d- 4 for d 〉 2 and n ≥ 2 except K(2, 2). It then follows that B(d,n) and K(d, n) are both super connected for any d ≥ 2 and n ≥ 1. 相似文献
3.
Jian Wang 《高校应用数学学报(英文版)》2008,23(3):345-350
A K1,k-factorization of λKm,n is a set of edge-disjoint K1,k-factors of λKm,n, which partition the set of edges of λKm,n. In this paper, it is proved that a sufficient condition for the existence of K1,k-factorization of λKm,n, whenever k is any positive integer, is that (1) m ≤ kn, (2) n ≤ km, (3) km-n = kn-m ≡ 0 (mod (k^2- 1)) and (4) λ(km-n)(kn-m) ≡ 0 (mod k(k- 1)(k^2 - 1)(m + n)). 相似文献
4.
Jian-pingOu Fu-jiZhang 《应用数学学报(英文版)》2003,19(3):505-510
An m-restricted edge cut is an edge cut that separates a connected graph into a disconnected one with no components having order less than m. m-restrict edge connectivity λm is the cardinality of a minimum m-restricted edge cut. Let G be a connected k-regular graph of order at least 2m that contains m-restricted edge cuts and X be a subgraph of G. Let θ(X) denote the number of edges with one end in X and the other not in X and ξm=min{θ(X) ;X is a connected vertex-induced subgraph of order m}.It is proved in this paper that if G has girth at least m/2 2,then λm≤ξm.The upper bound of λm is sharp. 相似文献
5.
Some results on R
2-edge-connectivity of even regular graphs 总被引:1,自引:0,他引:1
XuJunming 《高校应用数学学报(英文版)》1999,14(3):366-370
Let G be a connected k(≥3)-regular graph with girth g. A set S of the edges in G is called an Rredge-cut if G-S is disconnected and comains neither an isolated vertex nor a one-degree vertex. The R2-edge-connectivity of G, denoted by λ^n(G), is the minimum cardinality over all R2-edge-cuts, which is an important measure for fault-tolerance of computer interconnection networks. In this paper, λ^n(G)=g(2k-2) for any 2k-regular connected graph G (≠K5) that is either edge-transitive or vertex-transitive and g≥5 is given. 相似文献
6.
WANG Yingqian Department of Mathematics Zhejiang Normal University Jinhua China 《中国科学A辑(英文版)》2006,49(6):791-799
The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis. 相似文献
7.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
8.
E. Ballico 《Annali dell'Universita di Ferrara》1999,45(1):123-125
Fix integersg, k andt witht>0,k≥3 andtk<g/2−1. LetX be a generalk-gonal curve of genusg andR∈Pic
k
(X) the uniqueg
k
1
onX. SetL:=K
X⊗(R
*)⊗t.L is very ample. Leth
L:X→P(H
0(X, L)*) be the associated embedding. Here we prove thath
L(X) is projectively normal. Ifk≥4 andtk<g/2−2 the curveh
L(X) is scheme-theoretically cut out by quadrics.
The author was partially supported by MURST and GNSAGA of CNR (Italy). 相似文献
9.
Gordan Savin 《Israel Journal of Mathematics》1992,80(1-2):195-205
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L
2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP
f(g)=ΣH∩ΓΓ
f(γ{}itg) is an automorphic form on Γ\G. We show thatP
f is cuspidal in some cases, whenH ∩Γ\H is compact.
Partially supported by NSF Grant # DMS 9103608. 相似文献
10.
We analyze the structure of a continuous (or Borel) action of a connected semi-simple Lie group G with finite center and real rank at least 2 on a compact metric (or Borel) space X, using the existence of a stationary measure as the basic tool. The main result has the following corollary: Let P be a minimal parabolic subgroup of G, and K a maximal compact subgroup. Let λ be a P-invariant probability measure on X, and assume the P-action on (X,λ) is mixing. Then either λ is invariant under G, or there exists a proper parabolic subgroup Q⊂G, and a measurable G-equivariant factor map ϕ:(X,ν)→(G/Q,m), where ν=∫
K
kλdk and m is the K-invariant measure on G/Q. Furthermore, The extension has relatively G-invariant measure, namely (X,ν) is induced from a (mixing) probability measure preserving action of Q.
Oblatum 14-X-1997 & 18-XI-1998 / Published online: 20 August 1999 相似文献
11.
Definen
K
(λ) to be either ω, or the number of non-isomorphic models inK having cardinality α, whichever cardinal is larger. This paper contains a proof that for a congruence modular variety ⋎ of
algebras of countable similarity type, there are only six possible functionsn
⋎. It is also proved that ifn
K
(λ)≠2λ for some λ, andK is a universal Horn class of models for a countable language, thenK must satisfy two conditions, one of which is quite restrictive and requires that the members ofK are all in a certain sense Abelian.
Presented by B. Jonsson. 相似文献
12.
Raffaele Mosca 《Graphs and Combinatorics》2002,18(2):367-379
Moving from a well known result of Hammer, Hansen, and Simeone, we introduce a new graph invariant, say λ(G) referring to any graph G. It is a non-negative integer which is non-zero whenever G contains particular induced odd cycles or, equivalently, admits a particular minimum clique-partition. We show that λ(G) can be efficiently evaluated and that its determination allows one to reduce the hard problem of computing a minimum clique-cover
of a graph to an identical problem of smaller size and special structure. Furthermore, one has α(G)≤θ(G)−λ(G), where α(G) and θ(G) respectively denote the cardinality of a maximum stable set of G and of a minimum clique-partition of G.
Received: April 12, 1999 Final version received: September 15, 2000 相似文献
13.
We obtain a new upper bound for the sum Σ
h≤H
Δ
k
(N, h) when 1 ≤ H ≤ N, k ∈ ℕ, k ≥ 3, where Δ
k
(N, h) is the (expected) error term in the asymptotic formula for Σ
N<n≤2N
d
k
(n)d
k
(n + h), and d
k
(n) is the divisor function generated by ζ(s)
k
. When k = 3, the result improves, for H ≥ N
1/2, the bound given in a recent work of Baier, Browning, Marasingha and Zhao, who dealt with the case k = 3. 相似文献
14.
Let P(G, λ) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H, λ) = P(G, λ) implies H is isomorphic to G. Liu et al. [Liu, R. Y., Zhao, H. X., Ye, C. F.: A complete solution to a conjecture on chromatic uniqueness of complete
tripartite graphs. Discrete Math., 289, 175–179 (2004)], and Lau and Peng [Lau, G. C., Peng, Y. H.: Chromatic uniqueness of certain complete t-partite graphs. Ars Comb., 92, 353–376 (2009)] show that K(p − k, p − i, p) for i = 0, 1 are chromatically unique if p ≥ k + 2 ≥ 4. In this paper, we show that if 2 ≤ i ≤ 4, the complete tripartite graph K(p − k, p − i, p) is chromatically unique for integers k ≥ i and p ≥ k
2/4 + i + 1. 相似文献
15.
CHANG Yanxun 《中国科学A辑(英文版)》2000,43(2):128-140
Given any set K of positive integers and positive integer λ, let c(K,λ) denote the smallest integer such that v∈B(K,λ) for every integer v≥c(K,λ) that satisfies the congruences λv(v-1)≡0 (mod β(K) and λ(v-1)≡0 (mod α(K)). Let K0 be an equivalent set of K, k and k* be the smallest and the largest integers in K0. We prove that c(K,λ)≤exp exp{Q0}Qo=max{2(2p(ko)2-k2kk)p(ko)4,(Kk242y-k-2)(y2)}, whereand y=k*+k(k-1)+1. 相似文献
16.
Extremal probabilities for Gaussian quadratic forms 总被引:1,自引:0,他引:1
Denote by Q an arbitrary positive semidefinite quadratic form in centered Gaussian random variables such that E(Q)=1. We prove that for an arbitrary x>0, inf
Q
P(Q≤x)=P(χ2
n
/n≤x), where χ
n
2
is a chi-square distributed rv with n=n(x) degrees of freedom, n(x) is a non-increasing function of x, n=1 iff x>x(1)=1.5364…, n=2 iff x[x(2),x(1)], where x(2)=1.2989…, etc., n(x)≤rank(Q). A similar statement is not true for the supremum: if 1<x<2 and Z
1
,Z
2
are independent standard Gaussian rv's, then sup0≤λ≤1/2
P{λZ
1
2
+(1−λ)Z
2
2
≤x} is taken not at λ=0 or at λ=1/2 but at 0<λ=λ(x)<1/2, where λ(x) is a continuous, increasing function from λ(1)=0 to λ(2)=1/2, e.g. λ(1.5)=.15…. Applications of our theorems include asymptotic
quantiles of U and V-statistics, signal detection, and stochastic orderings of integrals of squared Gaussian processes.
Received: 24 June 2002 / Revised version: 26 January 2003
Published online: 15 April 2003
Research supported by NSA Grant MDA904-02-1-0091
Mathematics Subject Classification (2000): Primary 60E15, 60G15; Secondary 62G10 相似文献
17.
Asymptotic Upper Bounds for Ramsey Functions 总被引:5,自引:0,他引:5
We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nf
a
+1(d), where f
a
+1(d)=∫0
1(((1−t)1/(
a
+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(K
k
+
l
,K
n
)≤ (l+o(1))n
k
/(logn)
k
−1. In particular, r(K
k
, K
n
)≤(1+o(1))n
k
−1/(log n)
k
−2.
Received: May 11, 1998 Final version received: March 24, 1999 相似文献
18.
The paper deals with the structure of intermediate subgroups of the general linear group GL(n, k) of degree n over a field k of odd characteristic that contain a nonsplit maximal torus related to a radical extension of degree n of the ground field k. The structure of ideal nets over a ring that determine the structure of intermediate subgroups containinga transvection
is given. Let K = k( n?{d} ) K = k\left( {\sqrt[n]{d}} \right) be a radical degree-n extension of a field k of odd characteristic, and let T =(d) be a nonsplit maximal torus, which is the image of the multiplicative group of the field K under the regular embedding in G =GL(n, k). In the paper, the structure of intermediate subgroups H, T ≤ H ≤ G, that contain a transvection is studied. The elements of the matrices in the torus T = T (d) generate a subring R(d) in the field k.Let R be an intermediate subring, R(d) ⊆ R ⊆ k, d ∈ R. Let σR denote the net in which the ideal dR stands on the principal diagonal and above it and all entries of which beneath the principal diagonal are equal to R. Let σR denote the net in which all positions on the principal diagonal and beneath it are occupied by R and all entries above the principal diagonal are equal to dR. Let E(σR) be the subgroup generated by all transvections from the net group G(σR). In the paper it is proved that the product TE(σR) is a group (and thus an intermediate subgroup). If the net σ associated with an intermediate subgroup H coincides with σR,then TE(σR) ≤ H ≤ N(σR),where N(σR) is the normalizer of the elementary net group E(σR) in G. For the normalizer N(σR),the formula N(σR)= TG(σR) holds. In particular, this result enables one to describe the maximal intermediate subgroups. Bibliography: 13 titles. 相似文献
19.
In this paper we study three-color Ramsey numbers. Let K
i,j
denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G
1, G
2 and G
3, if r(G
1, G
2)≥s(G
3), then r(G
1, G
2, G
3)≥(r(G
1, G
2)−1)(χ(G
3)−1)+s(G
3), where s(G
3) is the chromatic surplus of G
3; (ii) (k+m−2)(n−1)+1≤r(K
1,k
, K
1,m
, K
n
)≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K
k,m
, K
k,m
, K
n
)≤c(n/logn), and r(C
2m
, C
2m
, K
n
)≤c(n/logn)
m/(m−1)
for sufficiently large n.
Received: July 25, 2000 Final version received: July 30, 2002
RID="*"
ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of
education ministry of China, and the foundations of Jiangsu Province
Acknowledgments. The authors are grateful to the referee for his valuable comments.
AMS 2000 MSC: 05C55 相似文献
20.
Abhijit Pal 《Proceedings Mathematical Sciences》2010,120(1):57-68
Let 1 → (K, K
1) → (G, N
G
(K
1)) → (Q, Q
1) → 1 be a short exact sequence of pairs of finitely generated groups with K
1 a proper non-trivial subgroup of K and K strongly hyperbolic relative to K
1. Assuming that, for all g ∈ G, there exists k
g
∈ K such that gK
1
g
−1 = k
g
K
1
k
g−1, we will prove that there exists a quasi-isometric section s: Q → G. Further, we will prove that if G is strongly hyperbolic relative to the normalizer subgroup N
G
(K
1) and weakly hyperbolic relative to K
1, then there exists a Cannon-Thurston map for the inclusion i: Γ
K
→ Γ
G
. 相似文献