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41.
42.
In this note we show how 1-factors in the middle two layers of the discrete cube can be used to construct 2-factors in the
Odd graph (the Kneser graph of (k − 1)-sets from a (2k − 1)-set). In particular, we use the lexical matchings of Kierstead and Trotter, and the modular matchings of Duffus, Kierstead
and Snevily, to give explicit constructions of two different 2-factorisations of the Odd graph.
This revised version was published online in September 2006 with corrections to the Cover Date. 相似文献
43.
A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices
is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same
degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations
on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces
on at most 11 vertices.
In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there
exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two
distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which
are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly
regular. 相似文献
44.
Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K5‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K3,3), M*(K5)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K5), M*(K5)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献
45.
Yao Ping HOU 《数学学报(英文版)》2005,21(4):955-960
A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated. 相似文献
46.
本文引入并研究一类新的广义集值强非线性拟变分不等式,讨论这类广义集值强非线性拟变分不等式解的存在性以及由算法所构造的迭代序列的收敛性.我们的结果改进和发展了Noor,Siddiqi和Ansari等人近期的一些主要结果. 相似文献
47.
48.
H. R. Ebrahimi-Vishki M. A. Pourabdollah 《Proceedings of the American Mathematical Society》1997,125(7):2171-2174
The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group.
49.
For given a graph H, a graphic sequence π = (d
1, d
2,..., d
n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K
5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to
be potentially K
5-graphic, where K
r is a complete graph on r vertices and K
r-e is a graph obtained from K
r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence
π to be potentially K
6-graphic.
Project supported by National Natural Science Foundation of China (No. 10401010). 相似文献
50.
In a graph, a cluster is a set of vertices, and two clusters are said to be non-intersecting if they are disjoint or one of them is contained in the other. A clustered graph C consists of a graph G and a set of non-intersecting clusters. In this paper, we assume that C has a compound planar drawing and each cluster induces a biconnected subgraph. Then we show that such a clustered graph admits a drawing in the plane such that (i) edges are drawn as straight-line segments with no edge crossing and (ii) the boundary of the biconnected subgraph induced by each cluster is a convex polygon. 相似文献