共查询到20条相似文献,搜索用时 31 毫秒
1.
Let G be a cubic graph of order 2n consisting of a cycle plus a perfect matching and let be the symmetric digraph obtained from G by replacing each edge of G by two opposite arcs. In this paper we study when can be decomposed into three hamiltonian circuits and in particular we prove that such a decomposition is impossible if n is even. 相似文献
2.
Z Füredi 《Journal of Combinatorial Theory, Series B》1983,34(2):187-190
Let f(n) denote the maximum number of edges of a graph on n vertices not containing a circuit of length 4. It is well known that . The old conjecture is proved for infinitely many q (whenever q = 2k). 相似文献
3.
We present solutions of seven graph equations involving the line graph, complement and n-th power operations. One such equation generalizes a result of M. Aigner. In addition, some comments are made about graphs satisfying . 相似文献
4.
Ioan Tomescu 《Journal of Combinatorial Theory, Series B》1980,28(2):127-141
In this paper some recursion formulas and asymptotic properties are derived for the numbers, denoted by N(p, q), of irreducible coverings by edges of the vertices of complete bipartite (labeled) graphs Kp,q. The problem of determining numbers N(p, q) has been raised by I. Tomescu (dans “Logique, Automatique, Informatique,” pp. 269–423, Ed. Acad. R.S.R., Bucharest, 1971). A result concerning the asymptotic behavior of the number of irreducible coverings by cliques of q-partite complete graphs is obtained and it is proved that , , and , where I(n) and M(n) are the maximal numbers of irreducible coverings, respectively, coverings by cliques of the vertices of an n-vertex graph, and C(n) is the maximal number of minimal colorings of an n-vertex graph. It is also shown that maximal number of irreducible coverings by n ? 2 cliques of the vertices of an n-vertex graph (n ≥ 4) is equal to 2n?2 ? 2 and this number of coverings is attained only for K2,n?2 and the value of is obtained, where I(n, n ? k) denotes the maximal number of irreducible coverings of an n-vertex graph by n ? k cliques. 相似文献
5.
George B Purdy 《Journal of Combinatorial Theory, Series A》1974,17(1):131-133
There are at most 2n spheres tangent to all n + 1 faces of an n-simplex. It has been shown that the minimum number of such spheres is if n is odd and if n is even. The object of this note is to show that this result is a consequence of a theorem in graph theory. 相似文献
6.
Paul Erdős Norbert Sauer Jonathan Schaer Joel Spencer 《Journal of Combinatorial Theory, Series B》1975,18(2):180-183
The graph G has star number n if any n vertices of G belong to a subgraph which is a star. Let f(n, k) be the smallest number m such that the complete graph on m vertices can be factorized into k factors with star number n. In the present paper we prove that . 相似文献
7.
R.J Cook 《Journal of Combinatorial Theory, Series B》1979,26(3):337-345
Let G be a planar graph having n vertices with vertex degrees d1, d2,…,dn. It is shown that . The main term in this upper bound is best possible. 相似文献
8.
Some results on the “evasiveness” of graph properties are obtained, extending the work of Rivest and Vuillemin. In particular, it is shown that any nontrivial monotone graph property on n vertices is at least ; particular stronger results are obtained for values of n that are powers of primes less than 14. A new result allowing interpolation among n values is obtained, as are some stronger results on restricted classes of properties. 相似文献
9.
In this paper we give fast algorithms for generating all maximal independent sets of three special classes of graphs—interval, circular-arc, and chordal graphs. The worst-case running times of our algorithms are O(n2 + β) for interval and circular-arc graphs, and for chordal graphs, where n, e, and α are the numbers of vertexes, edges, and maximal independent sets of a graph, and β is the sum of the numbers of vertexes of all maximal independent sets. Our algorithms compare favorably with the fastest known algorithm for general graphs which has a worst-case running time of . 相似文献
10.
W Fernandez de la Vega 《Journal of Combinatorial Theory, Series B》1983,35(3):328-332
For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if Tn denotes the random tournament on n vertices, then, as n → ∞. 相似文献
11.
《Journal of Combinatorial Theory, Series B》1986,40(2):187-195
The usual linear relaxation of the node-packing problem contains no useful information when the underlying graph G has the property of “bicriticality.” We consider a sparse random graph Gn(m) obtained in the usual way from a random directed graph with fixed out-degree m and show that the probability that Gn(2) is bicritical tends to as n→∞. This confirms a conjecture by G. R. Grimmett and W. R. Pulleyblank (Oper. Res. Lett., in press). 相似文献
12.
Edward A Bender Herbert S Wilf 《Journal of Algorithms in Cognition, Informatics and Logic》1985,6(2):275-282
The graph coloring problem is: Given a positive integer K and a graph G. Can the vertices of G be properly colored in K colors? The problem is NP-complete. The average behavior of the simplest backtrack algorithm for this problem is studied. Average run time over all graphs is known to be bounded. Average run time over all graphs with n vertices and q edges behaves like . It is shown that similar results hold for all higher moments of the run time distribution. For all graphs and for graphs where lim exists, the run time has a limiting disibution as n → ∞. 相似文献
13.
F. Götze 《Journal of multivariate analysis》1981,11(2):260-272
Let P(Θ, τ) 6 , θ ∈ Θ ? , τ ∈ T ? p denote a family of probability measures, where τ denotes the vector of nuisance parameters. Starting from randomized asymptotic maximum likelihood (as. m. l.) estimators for (θ, τ) we construct randomized estimators which are asymptotically median unbiased up to resp. test procedures which are as. similar of level (for testing θ = θ0, τ ∈ T against one sided alternatives). The estimation procedures are second-order efficient in the class of estimators which are median unbiased up to and the test procedures are second-order efficient in the class of tests which are as. of level . These results hold without any continuity condition on the family of probability measures. 相似文献
14.
On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804. 相似文献
15.
The usual Sobolev inequality in n, n ? 3, asserts that , with Sn being the sharp constant. This paper is concerned, instead, with functions restricted to bounded domains Ω ? n. Two kinds of inequalities are established: (i) If ? = 0 on ?Ω, then with and with . (ii) If ? ≠ 0 on ?Ω, then with . Some further results and open problems in this area are also presented. 相似文献
16.
Let A denote a decomposable symmetric complex valued n-linear function on Cm. We prove , where · denotes the symmetric product and ? the tensor product. As a consequence we have per , where M is a positive semidefinite Hermitian matrix and per denotes the permanent function. A sufficient condition for equality in the matrix inequality is that M is a nonnegative diagonal matrix. 相似文献
17.
18.
Hiroyuki Nakayama Takao Nishizeki Nobuji Saito 《Journal of Algorithms in Cognition, Informatics and Logic》1985,6(3):393-399
Nontrivial lower bounds are given for the computation time of various combinatorial problems on graphs under a linear or algebraic decision tree model. An bound is obtained for a “travelling salesman problem” on a weighted complete graph of n vertices. Moreover it is shown that the same bound is valid for the “subgraph detection problem” with respect to property P if P is hereditary and determined by components. Thus an bound is established in a unified way for a rather large class of problems. 相似文献
19.
Given a graph G, denote by tcl(G) the largest integer r for which G contains a TKr, a toplogical complete r-graph. We show that for every ? > 0 almost every graph G of order n satisfies 相似文献
20.
Guy Giraud 《Discrete Mathematics》1976,16(1):13-38
On determine le nombre maximum de triangles bicolores quand n tend vers l'infini, soit . On prouve aussi que, pour n assez grand, plus d'un triangle sur vingt-neuf est unicolore le methode suivie est susceptible de constituer une approche du probléme posé par une conjecture d'Erdos. Sos et Turan sur le nombre maximum de triangles tricolores. 相似文献