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21.
L''. Holá 《Set-Valued Analysis》2003,11(2):133-151
Our paper studies the topology of uniform convergence on compact sets on the space of densely continuous forms (introduced by Hammer and McCoy (1997)), usco and minimal usco maps. We generalize and complete results from Hammer and McCoy (1997) concerning the space D(X,Y) of densely continuous forms from X to Y. Let X be a Hausdorff topological space, (Y,d) be a metric space and D
k
(X,Y) the topology of uniform convergence on compact sets on D(X,Y). We prove the following main results: D
k
(X,Y) is metrizable iff D
k
(X,Y) is first countable iff X is hemicompact. This result gives also a positive answer to question 4.1 of McCoy (1998). If moreover X is a locally compact hemicompact space and (Y,d) is a locally compact complete metric space, then D
k
(X,Y) is completely metrizable, thus improving a result from McCoy (1998). We study also the question, suggested by Hammer and McCoy (1998), when two compatible metrics on Y generate the same topologies of uniform convergence on compact sets on D(X,Y). The completeness of the topology of uniform convergence on compact sets on the space of set-valued maps with closed graphs, usco and minimal usco maps is also discussed. 相似文献
22.
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
23.
In this paper we apply computer algebra (Maple) techniques to calculate Jones polynomial of graphs of K(2,q)-Torus knots. For this purpose, a computer program was developed. When a positive integer q is given, the program calculate Jones polynomial of graph of K(2,q)-Torus knots. 相似文献
24.
Vites Longani 《Southeast Asian Bulletin of Mathematics》2003,26(4):583-592
Consider a complete bipartite graph K(s, s) with p = 2s points. Let each line of the graph have either red or blue colour. The smallest number p of points such that K(s, s) always contains red K(m, n) or blue K(m, n) is called bipartite Ramsey number denoted by rb(K(m, n), K(m, n)). In this paper, we show that
AMS Subject Classifications (1991): 05C15, 05D10. 相似文献
(2) |
25.
A (K4 ? e)‐design on v + w points embeds a P3‐design on v points if there is a subset of v points on which the K4 ? e blocks induce the blocks of a P3‐design. It is shown that w ≥ ¾(v ? 1). When equality holds, the embedding design is easily constructed. In this paper, the next case, when w = ¾v, is settled with finitely many exceptions. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 352–366, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10044 相似文献
26.
In this note we show how coverings induced by voltage assignments can be used to produce packings of disjoint copies of the Hoffman‐Singleton graph into K50. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 408–412, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10049 相似文献
27.
In this article we study Hamilton cycles in sparse pseudo‐random graphs. We prove that if the second largest absolute value λ of an eigenvalue of a d‐regular graph G on n vertices satisfies and n is large enough, then G is Hamiltonian. We also show how our main result can be used to prove that for every c >0 and large enough n a Cayley graph X (G,S), formed by choosing a set S of c log5 n random generators in a group G of order n, is almost surely Hamiltonian. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 17–33, 2003 相似文献
28.
Suppose r ≥ 2 is a real number. A proper r‐flow of a directed multi‐graph is a mapping such that (i) for every edge , ; (ii) for every vertex , . The circular flow number of a graph G is the least r for which an orientation of G admits a proper r‐flow. The well‐known 5‐flow conjecture is equivalent to the statement that every bridgeless graph has circular flow number at most 5. In this paper, we prove that for any rational number r between 2 and 5, there exists a graph G with circular flow number r. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 304–318, 2003 相似文献
29.
30.
图的超常边连通度是图的边连通度概念的推广,对于n阶点可迁或正则边可迁的简单连通图来说,它的h阶超常边连通度λ_h一定存在(1≤h≤n/2)。本文证明了:当d_-正则的n_-阶点可迁简单连通图满足n≥6,d≥4且围长g≥5时,或d_-正则的n_-阶边可迁简单连通图满足n≥6,d≥4且围长g≥4时,对于任何的h:1≤h≤min{g-1,n/2},λ_h达到其最大可能值,即λ_h=hd-2(h-1)。 相似文献