共查询到20条相似文献,搜索用时 15 毫秒
1.
《Discrete Mathematics》1985,56(1):1-6
For any graph G we define the eccentric graph Ge on the same set of vertices, by joining two vertices in Ge if and only if one of the vertices has maximum possible distance from the other. The following results are given in this paper:
- (1)A few general properties of eccentric graphs.
- (2)A characterization of graphs G with Ge = Kp and with Ge = pK2.
- (3)A solution of the equation Ge = G¯.
2.
Liu Yanpei 《数学学报(英文版)》1989,5(1):64-79
The purpose of this paper which is a sequel of “ Boolean planarity characterization of graphs ” [9] is to show the following results.
- Both of the problems of testing the planarity of graphs and embedding a planar graph into the plane are equivalent to finding a spanning tree in another graph whose order and size are bounded by a linear function of the order and the size of the original graph, respectively.
- The number of topologically non-equivalent planar embeddings of a Hamiltonian planar graphG is τ(G)=2 c(H)?1, wherec (H) is the number of the components of the graphH which is related toG.
3.
In my talk, I will present some works done in the nineties on Laplacians on graphs: from eigenvalue problems to inverse problem for resistor networks. I will focus on the motivations and the main results as well as on the main ideas:
- •A differential topology point of view on the minor relation: a nice stratification associated to a finite graph Γ whose strata are associated to the minors of Γ
- •“Discrete” (graphs) versus “continuous” (Riemannian manifolds)
- •Stability of spectra with respect to singular limits: a finite dimensional theory of operators with domains (Von Neumann theory).
4.
We study conditions under which the characteristic vector of a normal lcQS-manifold is a torsion-forming or even a concircular vector field. We prove that the following assertions are equivalent:
- An lcQS-structure is normal, and its characteristic vector is a torsion-forming vector field.
- An lcQS-structure is normal, and its characteristic vector is a concircular vector field.
- An lcQS-structure is locally conformally cosymplectic and has a closed contact form.
5.
We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain:
- Geometric conditions ensuring the compactness of the underlying manifold (Bonnet–Myers type results);
- Volume estimates of metric balls;
- Gradient bounds and stochastic completeness for the heat semigroup generated by the sub-Laplacian;
- Spectral gap estimates.
6.
《Mathematical and Computer Modelling》1997,25(7):79-87
Research in graph theory has focused on studying the structure of graphs with the assumption that they are static. However, in many applications, the graphs that arise change with time, i.e., they are dynamic in nature. This is especially true of applications involving graph models in computer science. We present an expository study of dynamic graphs with the main driving force being practical applications. We first develop a formal classification of dynamic graphs. This taxonomy in the form of generalizations and extensions will in turn suggest new areas of application. Next, we discuss areas where dynamic graphs arise in computer science such as compilers, databases, fault-tolerance, artificial intelligence, and computer networks. Finally, we propose approaches that can be used for studying dynamic graphs. The main objective in any study of dynamic graphs should be to
- 1.(i) extend results developed for static graph theory to dynamic graphs,
- 2.(ii) study the properties that describe how a dynamic graph changes,
- 3.(iii) investigate problems and issues in dynamic graph theory that are raised by practical applications of dynamic graphs in computer science.
7.
In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n 1?1/[(d+1)/2]), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n 2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:
- the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
- whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
- the algorithm works well both theoretically and experimentally,
- the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
- the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).
8.
We show that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomial-bounded number of processors. We also show that several related problems lie in Random NC. These include:
- Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation;
- Constructing a maximum-cardinality matching;
- Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary;
- Constructing a maximums-t flow in a directed graph whose edge weights are given in unary.
9.
Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are
- classical circuit switch telephone networks (loss networks) and
- present-day wireless mobile networks.
- upper bounds for loss probabilities and
- analytic error bounds for the accuracy of the approximation for various performance measures.
- pure loss networks as under (i)
- GSM networks with fixed channel allocation as under (ii).
10.
《Applied Mathematics Letters》2003,16(5):657-662
The paper studies equation (1.1) in two cases:
- •(i)p ≡ 0,
- •(ii)p ≠ 0.
11.
Bruno Klingler 《Inventiones Mathematicae》2013,192(2):257-286
While Margulis’ superrigidity theorem completely describes the finite dimensional linear representations of lattices of higher rank simple real Lie groups, almost nothing is known concerning the representation theory of complex hyperbolic lattices. The main result of this paper (Theorem 1.3) is a strong rigidity theorem for a certain class of cocompact arithmetic complex hyperbolic lattices. It relies on the following two ingredients:
- Theorem 1.6 showing that the representations of the topological fundamental group of a compact Kähler manifold X are controlled by the global symmetric differentials on X.
- An arithmetic vanishing theorem for global symmetric differentials on certain compact ball quotients using automorphic forms, in particular deep results of Clozel on base change (Theorem 1.11).
12.
Sean McGuinness 《Combinatorica》1994,14(3):321-334
A greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empty. It has recently been shown that any greedy clique decomposition of a graph of ordern has at mostn 2/4 cliques. In this paper, we extend this result by showing that for any positive integerp, 3≤p any clique decomposisitioof a graph of ordern obtained by removing maximal cliques of order at leastp one by one until none remain, in which case the remaining edges are removed one by one, has at mostt p-1( n ) cliques. Heret p-1( n ) is the number of edges in the Turán graph of ordern, which has no complete subgraphs of orderp. In connection with greedy clique decompositions, P. Winkler conjectured that for any greedy clique decompositionC of a graphG of ordern the sum over the number of vertices in each clique ofC is at mostn 2/2. We prove this conjecture forK 4-free graphs and show that in the case of equality forC andG there are only two possibilities:
- G?K n/2,n/2
- G is complete 3-partite, where each part hasn/3 vertices.
13.
Frédéric Maire 《Graphs and Combinatorics》1994,10(2-4):263-268
A graph istriangulated if it has no chordless cycle with at least four vertices (?k ≥ 4,C k ?G). These graphs Jhave been generalized by R. Hayward with theweakly triangulated graphs $(\forall k \geqslant 5,C_{k,} \bar C_k \nsubseteq G)$ . In this note we propose a new generalization of triangulated graphs. A graph G isslightly triangulated if it satisfies the two following conditions;
- G contains no chordless cycle with at least 5 vertices.
- For every induced subgraphH of G, there is a vertex inH the neighbourhood of which inH contains no chordless path of 4 vertices.
14.
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we extend the following four topics from (un)directed graphs to bidirected graphs:
- –Erdős–Gallai-type results: characterization of net-degree sequences,
- –Havel–Hakimi-type results: complete sets of degree-preserving operations,
- –Extremal degree sequences: characterization of uniquely realizable sequences, and
- –Enumerative aspects: counting formulas for net-degree sequences.
15.
With graphs considered as natural models for many network design problems, edge connectivity κ′(G) and maximum number of edge-disjoint spanning trees τ(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G (see Cunningham, in J ACM 32:549–561, 1985; Matula, in Proceedings of 28th Symposium Foundations of Computer Science, pp 249–251, 1987, among others). Mader (Math Ann 191:21–28, 1971) and Matula (J Appl Math 22:459–480, 1972) introduced the maximum subgraph edge connectivity \({\overline{\kappa'}(G) = {\rm max} \{\kappa'(H) : H {\rm is} \, {\rm a} \, {\rm subgraph} \, {\rm of} G \}}\) . Motivated by their applications in network design and by the established inequalities $$\overline{\kappa'}(G) \ge \kappa'(G) \ge \tau(G),$$ we present the following in this paper:
- For each integer k > 0, a characterization for graphs G with the property that \({\overline{\kappa'}(G) \le k}\) but for any edge e not in G, \({\overline{\kappa'}(G + e) \ge k+1}\) .
- For any integer n > 0, a characterization for graphs G with |V(G)| = n such that κ′(G) = τ(G) with |E(G)| minimized.
16.
《Annals of Pure and Applied Logic》1988,37(3):205-248
We develop a series of Ehrenfeucht games and prove the following results:
- 1.(i) The first order theory of the divisible and indecomposable p-group, the first order theory of the group of rational numbers with denominators prime to p and the first order theory of a cyclic group of prime power order can be decided in 22cn log n Turing time.
- 2.(ii) The first order theory of the direct sum of countably many infinite cyclic groups, the first order theory of finite Abelian groups and the first order theory of all Abelian groups can be decided in 22dn Turing space.
17.
Miroslaw Truszczyski 《Journal of Graph Theory》1984,8(1):171-176
In this note the second moment of the vertex degree sequence of planar graphs is considered. We prove that
- 1 If G is an outerplanar graph of order n ? 3 then
- 2 If G is a planar graph of order n ? 4 then
18.
《Mathematical and Computer Modelling》2000,31(10-12):157-163
An auto-sleep system is defined by the following two properties:
- 1.(i) a call for the system occurs randomly and intermittently
- 2.(ii) the system automatically goes to sleep if there occurs no call during a prespecified time T.
- 1.(a) sleep
- 2.(b) warm-up
- 3.(c) nonusage
- 4.(d) usage.
19.
Lawrence J. Risman 《Israel Journal of Mathematics》1977,28(1-2):113-128
Theorem 1
Let q=char(k). Let M be a subfield of D which is Galois over K of degree m with Galois group H.- If q/m then H has a normal q-Sylow subgroup.
- Iq q ? m then H is an abelian group with one or two generators, an extension of a cyclic group by a cyclic group of order e where k contains a primitive e-th root of unity.
Theorem 2
If n is divisible by the square of a prime p≠char(k) and k does not contain a primitive p-th root of unity, then k(X) is not a crossed product. 相似文献20.
Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects:
- equivalence classes of α-invariant K-connections on X
- α-invariant gauge classes of K-connections on X, and
- α-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic K ?-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).