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1.
In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs,
and a sufficient condition for a graph to be k-locally independent well-dominated. Using these results we show that the irredundance number, the domination number and the
independent domination number can be computed in polynomial time within several classes of graphs, e.g., the class of locally
well-dominated graphs.
Received: September 13, 2001 Final version received: May 17, 2002
RID="*"
ID="*" Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093)
RID="†"
ID="†" Supported by RUTCOR
RID="*"
ID="*" Supported by the INTAS and the Belarus Government (Project INTAS-BELARUS 97-0093)
05C75, 05C69
Acknowledgments. The authors thank the referees for valuable suggestions. 相似文献
2.
PETERC.B.LAM 《应用数学学报(英文版)》1998,14(2):193-196
1.IntroductionFOragraphG=(V,E)oforderp,aonetoonemappingfromVinto{l,2,',p}iscalledanumberingofG.Definition1.1.SupposefisanumberingofG.LetBj(G)=(u57teif(u)--f(v)l.ThebandwidthofG,denotedbyB(G),isdefinedbyB(G)=min{Bf(G)IfisanumberingofG}.Thebandwidthproblemofgraphshasbecomeveryimportantsincethemid-sixties(see[21or[4]).Itisverydifficulttodeterminethebandwidthofagraph.GareyetallllshowedthatthebandwidthproblemisNP-completeevenifitisrestrictedtotreeswithmaximumdegree3.Soitisinterestingtoe… 相似文献
3.
Narong Punnim 《Graphs and Combinatorics》2002,18(4):781-785
Let ω(G) be the clique number of a graph G. We prove that if G runs over the set of graphs with a fixed degree sequence d, then the values ω(G) completely cover a line segment [a,b] of positive integers. For an arbitrary graphic degree sequence d, we define min(ω,d) and max(ω,d) as follows:
where is the graph of realizations of d.
Thus the two invariants a:=min(ω,d) and b:=max(ω,d) naturally arise. For a graphic degree sequence d=r
n
:=(r,r,…,r) where r is the vertex degree and n is the number of vertices, the exact values of a and b are found in all situations. Since the independence number, α(G)=ω(Gˉ), we obtain parallel results for the independence number of graphs.
Received: October, 2001 Final version received: July 25, 2002
RID="*"
ID="*" Work supported by The Thailand Research Fund, under the grant number BRG/09/2545 相似文献
4.
Dedicated to the memory of Paul Erdős
We provide an elementary proof of the fact that the ramsey number of every bipartite graph H with maximum degree at most is less than . This improves an old upper bound on the ramsey number of the n-cube due to Beck, and brings us closer toward the bound conjectured by Burr and Erdős. Applying the probabilistic method
we also show that for all and there exists a bipartite graph with n vertices and maximum degree at most whose ramsey number is greater than for some absolute constant c>1.
Received December 1, 1999
RID="*"
ID="*" Supported by NSF grant DMS-9704114
RID="**"
ID="**" Supported by KBN grant 2 P03A 032 16 相似文献
5.
Maximal Energy Bipartite Graphs 总被引:1,自引:0,他引:1
Given a graph G, its energy E(G) is defined to be the sum of the absolute values of the eigenvalues of G. This quantity is used in chemistry to approximate the total π-electron energy of molecules and in particular, in case G is bipartite, alternant hydrocarbons. Here we show that if G is a bipartite graph with n vertices, then
must hold, characterize those bipartite graphs for which this bound is sharp, and provide an infinite family of maximal energy
bipartite graphs.
Received: December 1, 2000 Final version received: August 28, 2001
RID="*"
ID="*" The author thanks the Swedish Natural Science Research Council (NFR) – grant M12342-300 – for its support.
Acknowledgments. The authors would like to thank Ivan Gutman for encouraging them to write this paper, and for helpful discussions on this
topic. They also would like to thank Edwin van Dam for his reference concerning connected bipartite regular graphs with four
eigenvalues. 相似文献
6.
7.
We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously.
In particular, we show that the n-fold product of nonabelian free groups cannot act properly discontinuously on ℝ2
n
−1.
Oblatum 19-I-2001 & 29-V-2002?Published online: 5 September 2002
RID="*"
ID="*"All three authors gratefully acknowledge the support by the National Science Foundation. 相似文献
8.
Summary. Some observations are made on abstract error estimates for Galerkin approximations based on Babuška-Brezzi conditions. A
basic error estimate due to Babuška is sharpened by means of an identity that for any nontrivial idempotent operator P. Some remarks are also made on the Brezzi's theory for mixed variational problems and their Galerkin approximations.
Received March 1, 2000 / Revised version received September 28, 2000 / Published online June 17, 2002
RID="*"
ID="*" This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236
Correspondence to: J. Xu 相似文献
9.
We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem
1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li-Yau ’s gradient estimate.
As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also
show that the equality holds in Li-Yau’s gradient estimate, for some positive solution to the heat equation, at some positive
time, implies that the complete Riemannian manifold with nonnegative Ricci curvature is isometric to ℝ
n
.In the second section we derive a dual entropy formula which, to some degree, connects Hamilton’s entropy with Perelman ’s
entropy in the case of Riemann surfaces. 相似文献
10.
David A. Madore 《manuscripta mathematica》2003,110(2):171-185
We study R-equivalence on cubic hypersurfaces, and explain how to construct families of rational curves. We show that for a smooth cubic
hypersurface defined over a number field K, the Chow group of zero-cycles of degree 0 is trivial in almost every place of K.
Received: 20 March 2002 Published online: 24 January 2003 相似文献
11.
This paper introduces an exact primal augmentation algorithm for solving general linear integer programs. The algorithm iteratively
substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine
inequalities. We prove that various versions of our algorithm are finite. It is a major concern in this paper to show how
the subproblem of replacing a column can be accomplished effectively. An implementation of the presented algorithms is given.
Computational results for a number of hard 0/1 integer programs from the MIPLIB demonstrate the practical power of the method.
Received: April 23, 2001 / Accepted: May 2002
Published online: March 21, 2003
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="#"
ID="#"Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET
program TMR ERB FMRX-CT98-0202.
Mathematics Subject Classification (1991): 90C10 相似文献
12.
If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that π1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In
particular, we show this for tight essential laminations with solid torus guts. We also show that pseudo-Anosov flows induce
actions on circles. In all cases, these actions can be made into faithful ones, so π1(M) is isomorphic to a subgroup of Homeo(S
1). In addition, we show that the fundamental group of the Weeks manifold has no faithful action on S
1. As a corollary, the Weeks manifold does not admit a tight essential lamination with solid torus guts, a pseudo-Anosov flow,
or a taut foliation. Finally, we give a proof of Thurston’s universal circle theorem for taut foliations based on a new, purely
topological, proof of the Leaf Pocket Theorem.
Oblatum 20-III-2002 & 30-IX-2002?Published online: 18 December 2002
RID="*"
ID="*"Both authors partially supported by the U.S. National Science Foundation. 相似文献
13.
Imre Patyi 《Mathematische Annalen》2003,326(3):417-441
Let X be a complex Banach space with a countable unconditional basis, Ω⊂X pseudoconvex open, G a complex Banach Lie group. We show that a Runge–type approximation hypothesis on X, G (which we also prove for G a solvable Lie group) implies that any holomorphic cocycle on Ω with values in G can be resolved holomorphically if it can be resolved continuously.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L05, 32E30, 46G20
RID="*"
ID="*" Kedves Szímuskának.
RID="*"
ID="*" To my dear Wife. 相似文献
14.
15.
Sergei. S. Goncharov Valentina. S. Harizanov Julia. F. Knight Charles F. D. McCoy 《Archive for Mathematical Logic》2003,42(3):279-291
Let 𝒜 be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of 𝒜 in
which the image of R (?R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on 𝒜 and R, a necessary and sufficient condition for the existence of a computable copy ℬ of 𝒜 in which the image of R (?R, resp.) is simple (immune, resp.).
Received: 4 February 2001 Published online: 5 November 2002
RID="*"
ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.
RID="*"
ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.
RID="*"
ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899. 相似文献
16.
I. R. Kayumov 《Russian Mathematics (Iz VUZ)》2012,56(4):27-37
For p ≥ 2 we obtain bounds for L
p
-norms of the Fourier transform of real parts of simple partial fractions. For even p our estimate is sharp. We also prove a new inequality for L
p
-norms of simple partial fractions which in some cases is stronger than the corresponding inequality obtained by V. Yu. Protasov. 相似文献
17.
Shin-ichi Kobayashi 《Inventiones Mathematicae》2003,152(1):1-36
We give a new formulation in Iwasawa theory for elliptic curves at good supersingular primes. This formulation is similar
to Mazur’s at good ordinary primes. Namely, we define a new Selmer group, and show that it is of Λ-cotorsion. Then we formulate
the Iwasawa main conjecture as that the characteristic ideal is generated by Pollack’s p-adic L-function. We show that this main conjecture is equivalent to Kato’s and Perrin-Riou’s main conjectures. We also prove an
inequality in the main conjecture by using Kato’s Euler system. In terms of the λ- and the μ-invariants of our Selmer group,
we specify the numbers λ and μ in the asymptotic formula for the order of the Tate-Shafarevich group by Kurihara and Perrin-Riou.
Oblatum 17-VI-2002 & 2-IX-2002?Published online: 18 December 2002 相似文献
18.
Fedor V. Fomin 《Graphs and Combinatorics》2003,19(1):91-99
We prove that for every 2-connected planar graph the pathwidth of its geometric dual is less than the pathwidth of its line
graph. This implies that pathwidth(H)≤ pathwidth(H
*)+1 for every planar triangulation H and leads us to a conjecture that pathwidth(G)≤pathwidth(G
*)+1 for every 2-connected graph G.
Received: May 8, 2001 Final version received: March 26, 2002
RID="*"
ID="*" I acknowledge support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies)
and support by the RFBR grant N01-01-00235.
Acknowledgments. I am grateful to Petr Golovach, Roland Opfer and anonymous referee for their useful comments and suggestions. 相似文献
19.
A minimal defining set of a Steiner triple system on v points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v+1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets.
For example, for Steiner triple systems on 3
n
points, we construct minimal defining sets of volumes varying by as much as 7
n−2
.
Received: September 16, 2000 Final version received: September 13, 2001
RID="*"
ID="*" Research supported by the Australian Research Council A49937047, A49802044 相似文献
20.
S. Wehmeier 《Lithuanian Mathematical Journal》2006,46(3):371-383
We show that the Turán-Kubilius inequality holds for additive arithmetical semigroups satisfying the following conditions:
G(n) = q
n
(A+O(1/ln n)) (where A > 0 and q > 1) for the number of elements of degree n and P(n) = O(q
n
/n) for the number of prime elements of degree n. This is an improvement of a result of Zhang. We also give some variants of the inequality under some stronger or weaker
assumptions and applications for the prime divisor function ω and related functions.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 457–471, July–September, 2006. 相似文献