共查询到20条相似文献,搜索用时 493 毫秒
1.
Dedicated to the memory of Paul Erdős
A graph is called H-free if it contains no induced copy of H. We discuss the following question raised by Erdős and Hajnal. Is it true that for every graph H, there exists an such that any H-free graph with n vertices contains either a complete or an empty subgraph of size at least ? We answer this question in the affirmative for a special class of graphs, and give an equivalent reformulation for tournaments.
In order to prove the equivalence, we establish several Ramsey type results for tournaments.
Received August 22, 1999
RID="*"
ID="*" Supported by a USA Israeli BSF grant, by a grant from the Israel Science Foundation and by the Hermann Minkowski Minerva
Center for Geometry at Tel Aviv University.
RID="†"
ID="†" Supported by NSF grant CR-9732101, PSC-CUNY Research Award 663472, and OTKA-T-020914.
RID="‡"
ID="‡" Supported by TKI grant Stochastics@TUB, and OTKA-T-026203. 相似文献
2.
We show that every 6-edge connected graph admits a circulation whose range lies in the interval [1,3).
Received March 29, 2000
RID="*"
ID="*" Supported by NATO-CNR Fellowship; this work was done while the author was visiting the Dept. of Mathematics and Statistics
at Simon Fraser University, Canada.
RID="†"
ID="†" Supported by a National Sciences and Engineering Research Council Research Grant 相似文献
3.
Dedicated to the memory of Paul Erdős
Let H be a simple graph having no isolated vertices. An (H,k)-vertex-cover of a simple graph G = (V,E) is a collection of subgraphs of G satisfying
1. , for all i = 1, ..., r,
2. ,
3. , for all , and
4. each is in at most k of the . We consider the existence of such vertex covers when H is a complete graph, , in the context of extremal and random graphs.
Received October 31, 1999
RID="*"
ID="*" Supported in part by NSF grant DMS-9627408.
RID="†"
ID="†" Supported in part by NSF grant CCR-9530974.
RID="‡"
ID="‡" Supported in part by OTKA Grants T 030059 and T 29074, FKFP 0607/1999 and by the Bolyai Foundation.
RID="§"
ID="§" Supported in part by NSF grant DMS-9970622. 相似文献
4.
Dedicated to the memory of Paul Erdős
We extend a result of J. Alexander and D. Zagier on the Garsia entropy of the Erdős measure. Our investigation heavily relies
on methods from combinatorics on words. Furthermore, we introduce a new singular measure related to the Farey tree.
Received October 7, 1999
RID="†"
ID="†" This author is supported by the START-project Y96-MAT of the Austrian Science Fund
RID="‡"
ID="‡" This author is supported by the Austrian Science Fund (FWF) grant P14200-MAT
RID="*"
ID="*" This author is supported by the Austrian Science Fund (FWF) grant S8307-MAT 相似文献
5.
We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle that separates the
surface into two pieces. As a special case, every triangulation of the double torus in which every noncontractible cycle has
length at least 4 has a noncontractible cycle that separates the surface into two pieces.
Received: May 22, 2001 Final version received: August 22, 2002
RID="*"
ID="*" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070613
RID="†"
ID="†" Supported by NSF Grants Numbers DMS-9622780 and DMS-0070430 相似文献
6.
Dedicated to the memory of Paul Erdős
Suppose we have a finite collection of closed convex sets in the plane, (which without loss of generality we can take to be
polygons). Suppose further that among any four of them, some three have non-empty intersection. We show that 13 points are
sufficient to meet every one of the convex sets.
Received October 27, 1999/Revised April 11, 2000
RID="*"
ID="*" Supported by grant OTKA-T-029074.
RID="†"
ID="†" Supported by NSF grant DMS-99-70071, OTKA-T-020914 and OTKA-F-22234. 相似文献
7.
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
8.
It is proved that, for any ɛ>0 and n>n
0(ɛ), every set of n points in the plane has at most triples that induce isosceles triangles. (Here e denotes the base of the natural logarithm, so the exponent is roughly 2.136.) This easily implies the best currently known
lower bound, , for the smallest number of distinct distances determined by n points in the plane, due to Solymosi–Cs. Tóth and Tardos.
Received: February, 2002 Final version received: September 15, 2002
RID="*"
ID="*" Supported by NSF grant CCR-00-86013, PSC-CUNY Research Award 63382-00-32, and OTKA-T-032452
RID="†"
ID="†" Supported by OTKA-T-030059 and AKP 2000-78-21 相似文献
9.
Dedicated to the memory of Paul Erdős
In [9] Thomassen proved that a -connected graph either contains k vertex disjoint odd cycles or an odd cycle cover containing at most 2k-2 vertices, i.e. he showed that the Erdős–Pósa property holds for odd cycles in highly connected graphs. In this paper, we
will show that the above statement is still valid for 576k-connected graphs which is essentially best possible.
Received November 17, 1999
RID="*"
ID="*" This work was supported by a post-doctoral DONET grant.
RID="†"
ID="†" This work was supported by an NSF-CNRS collaborative research grant.
RID="‡"
ID="‡" This work was performed while both authors were visiting the LIRMM, Université de Montpellier II, France. 相似文献
10.
Graph Orientations with Edge-connection and Parity Constraints 总被引:2,自引:0,他引:2
Parity (matching theory) and connectivity (network flows) are two main branches of combinatorial optimization. In an attempt
to understand better their interrelation, we study a problem where both parity and connectivity requirements are imposed.
The main result is a characterization of undirected graphs G = (V,E) having a k-edge-connected T-odd orientation for every subset with |E| + |T| even. (T-odd orientation: the in-degree of v is odd precisely if v is in T.) As a corollary, we obtain that every (2k)-edge-connected graph with |V| + |E| even has a (k-1)-edge-connected orientation in which the in-degree of every node is odd. Along the way, a structural characterization will
be given for digraphs with a root-node s having k edge-disjoint paths from s to every node and k-1 edge-disjoint paths from every node to s.
Received December 14, 1998/Revised January 12, 2001
RID="*"
ID="*" Supported by the Hungarian National Foundation for Scientific Research, OTKA T029772. Part of research was done while
this author was visiting EPFL, Lausanne, June, 1998.
RID="†"
ID="†" Supported by the Hungarian National Foundation for Scientific Research, OTKA T029772 and OTKA T030059. 相似文献
11.
Say that a function π:n
<ω
→n (henceforth called a predictor) k-constantly predicts a real xn
ω
if for almost all intervals I of length k, there is iI such that x(i)=π(x↾i). We study the k-constant prediction number v
n
const
(k), that is, the size of the least family of predictors needed to k-constantly predict all reals, for different values of n and k, and investigate their relationship.
Received: 27 June 2001 / Revised version: 10 September 2001 /
Published online: 10 October 2002
RID="*"
ID="*" Supported by Grant–in–Aid for Scientific Research (C)(2)12640124, Japan Society for the Promotion of Science
RID="†"
ID="†" Supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Publication 762 相似文献
12.
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
13.
Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms.
Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002
RID="*"
ID="*" Supported by the National Science Foundation under grant DMS-9870187
RID="**"
ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160 相似文献
14.
Norbert Sauer 《Combinatorica》2001,21(2):293-308
Dedicated to the memory of Paul Erdős
Erdős, Hajnal and Pósa exhibited in [1] a partition (U,D) of the edges of the Rado graph which is a counterexample to . They also obtained that if every vertex of a graph has either in or in the complement of finite degree then .
We will characterize all graphs so that .
Received October 29, 1999
RID="†"
ID="†" Supported by NSERC of Canada Grant #691325. 相似文献
15.
Dedicated to the Memory of Paul Erdős
We generalize the multiparty communication model of Chandra, Furst, and Lipton (1983) to functions with b-bit output (b = 1 in the CFL model). We allow the players to receive up to b - 1 bits of information from an all-powerful benevolent Helper who can see all the input. Extending results of Babai, Nisan,
and Szegedy (1992) to this model, we construct families of explicit functions for which bits of communication are required to find the "missing bit", where n is the length of each player's input and k is the number of players. As a consequence we settle the problem of separating the one-way vs. multiround communication complexities
(in the CFL sense) for players, extending a result of Nisan and Wigderson (1991) who demonstrated this separation for k = 3 players. As a by-product we obtain lower bounds for the multiparty complexity (in the CFL sense) of new families of explicit boolean functions (not derivable
from BNS). The proofs exploit the interplay between two concepts of multicolor discrepancy; discrete Fourier analysis is the
basic tool. We also include an unpublished lower bound by A. Wigderson regarding the one-way complexity of the 3-party pointer
jumping function.
Received November 12, 1998
RID="*"
ID="*" Supported in part by NSA grant MSPR-96G-184.
RID="†"
ID="†" Supported in part by an NSF Graduate Fellowship. 相似文献
16.
Summary. Impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current
flows and voltages on its surface. In its most general form impedance tomography is quite ill-posed, but when additional a-priori
information is admitted the situation changes dramatically. In this paper we consider the case where the goal is to find a
number of small objects (inhomogeneities) inside an otherwise known conductor. Taking advantage of the smallness of the inhomogeneities,
we can use asymptotic analysis to design a direct (i.e., non-iterative) reconstruction algorithm for the determination of
their locations. The viability of this direct approach is documented by numerical examples.
Received May 28, 2001 / Revised version received March 15, 2002 / Published online July 18, 2002
RID="⋆"
ID="⋆" Supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HA 2121/2-3
RID="⋆⋆"
ID="⋆⋆" Supported by the National Science Foundation under grant DMS-0072556
Mathematics Subject Classification (2000): 65N21, 35R30, 35C20 相似文献
17.
Bojan Mohar 《Combinatorica》2001,21(3):395-401
It is proved that the decision problem about the existence of an embedding of face-width 3 of a given graph is NP-complete. A similar result is proved for some related decision problems. This solves a problem raised by Neil Robertson.
Received July 6, 1998
RID="*"
ID="*" Supported in part by the Ministry of Science and Technology of Slovenia, Research Project J1–0502–0101–98. 相似文献
18.
19.
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
20.
Imre Z. Ruzsa 《Combinatorica》2001,21(2):279-291
To the memory of Pál Erdős
Thirty years ago I read the following question of Erdőos [4]:
"Does there exist a sequence with so that every sufficiently large number is of the form ? $10"
I sent my solution to Erdős in a letter (in Hungarian). He translated my letter into English and sent it to the Canadian Math.
Bulletin; this became my first paper to appear.
In this paper we will find, among others, the best value of the constant c in the above question, which was also asked by Erdős.
Received March 30, 2000
RID="*"
ID="*" Supported by Hungarian National Foundation for Scientific Research, Grants No. T 025617 and T 29759. 相似文献