共查询到20条相似文献,搜索用时 15 毫秒
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Let G be a planar graph with maximum degree Δ. It is proved that if Δ ≥ 8 and G is free of k-cycles for some k ∈ {5,6}, then the total chromatic number χ′′(G) of G is Δ + 1.
This work is supported by a research grant NSFC(60673047) and SRFDP(20040422004) of China.
Received: February 27, 2007. Final version received: December 12, 2007. 相似文献
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Arthur W. Apter 《Archive for Mathematical Logic》2002,41(8):705-719
We prove three theorems concerning Laver indestructibility, strong compactness, and measurability. We then state some related
open questions.
Received: 11 December 1999 / Revised version: 17 September 2000 / Published online: 2 September 2002
Mathematics Subject classification (2000): 03E35, 03E55
Keywords or phrases: Measurable cardinal – Strongly compact cardinal – Supercompact cardinal – Indestructibility 相似文献
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In this note we prove that the game chromatic index χ
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′(G) of a graph G of arboricity k is at most Δ + 3k − 1. This improves a bound obtained by Cai and Zhu [J. Graph Theory 36 (2001), 144–155] for k-degenerate graphs.
Tomasz Bartnicki: Research of the first author is supported by a PhD grant from Polish Ministry of Science and Higher Education
N201 2128 33.
Received: November 1, 2006. Final version received: December 22, 2007. 相似文献
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Marián Trenkler 《Graphs and Combinatorics》2001,17(1):171-175
We deal with complete k-partite hypergraphs and we show that for all k≥2 and n≠2,6 its hyperedges can be labeled by consecutive integers 1,2,…,n
k
such that the sum of labels of the hyperedges incident to (k−1) particular vertices is the same for all (k−1)-tuples of vertices from (k−1) independent sets.
Received: December 8, 1997 Final version received: July 26, 1999 相似文献
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Carmine Di Fiore Stefano Fanelli Filomena Lepore Paolo Zellini 《Numerische Mathematik》2003,94(3):479-500
Summary. In this paper a new class of quasi-Newton methods, named ℒQN, is introduced in order to solve unconstrained minimization problems. The novel approach, which generalizes classical BFGS methods, is based on a Hessian updating formula involving an algebra ℒ of matrices simultaneously diagonalized by a fast
unitary transform. The complexity per step of ℒQN methods is O(n log n), thereby improving considerably BFGS computational efficiency. Moreover, since ℒQN's iterative scheme utilizes single-indexed arrays, only O(n) memory allocations are required. Global convergence properties are investigated. In particular a global convergence result
is obtained under suitable assumptions on f. Numerical experiences [7] confirm that ℒQN methods are particularly recommended for large scale problems.
Received December 30, 2001 / Revised version received December 20, 2001 /
Published online November 27, 2002
Mathematics Subject Classification (1991): 65K10
Correspondence to: P. Zellini 相似文献
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A claw is a rooted tree whose each branch is a directed path starting at the root. We prove that each rotational tournament on 2n+1 vertices contains all claws with 2n edges and at most n branches.
Received: December 15, 1999 Final version received: April 18, 2001
Acknowledgements. The authors wish to express their gratitude to the referee for valuable remarks, suggestions and comments that led to an
improved paper. 相似文献
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Olivier Guibé 《Annali di Matematica Pura ed Applicata》2002,180(4):441-449
We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem -div(a(x,Du))=μ in Ω, u=0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω.
Received: December 27, 2000 Published online: December 19, 2001 相似文献
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Sean McGuinness 《Graphs and Combinatorics》2001,17(1):135-148
Let ? be the family of finite collections ? where ? is a collection of bounded, arcwise connected sets in ℝ2 where for any S,T∈? such that S∩T≠?, it holds that S∩T is arcwise connected. Given ? is triangle-free, and provided the chromatic number χ(G) of the intersection graph G=G(?) of ? is sufficiently large, there exists α>1 independent of ? such that there is a subcollection ?′⊂? of at most 5 sets with the property that the sets of ? surrounded by ?′ induce an intersection graph H where .
Received: November 13, 1995 Final version received: December 3, 1998 相似文献
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A geometric graph any two line segments of which intersect is called an intersector. This notion will be generalized in order to obtain new results which are not true for this (restricted) category.
Received: December 8, 1997 Final version received: January 12, 2000 相似文献
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Online algorithms: a survey 总被引:5,自引:0,他引:5
Susanne Albers 《Mathematical Programming》2003,97(1-2):3-26
During the last 15 years online algorithms have received considerable research interest. In this survey we give an introduction
to the competitive analysis of online algorithms and present important results. We study interesting application areas and
identify open problems.
Received: December 1, 2002 / Accepted: April 28, 2003
Published online: May 28, 2003
Mathematics Subject Classification (1991): 68W25, 68W40 相似文献
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Kyo Fujita 《Graphs and Combinatorics》2002,18(3):447-478
We show that if G is a 3-connected hamiltonian graph of order at least 5, then there exists a hamiltonian cycle C of G such that the number of contractible edges of G which are on C is greater than or equal to .
Received: July 31, 2000 Final version received: December 12, 2000
Acknowledgments. I would like to thank Professor Yoshimi Egawa for the help he gave to me during the preparation of this paper. 相似文献