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1.
Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ2(G)n+k-1. Let v1,…,vk be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C1,…,Ck with viV(Ci) for all 1ik.Then G has k vertex-disjoint cycles such that
- (i) for all 1ik.
- (ii) , and
- (iii) At least k-1 of the k cycles are triangles.
Keywords: Degree sum condition; Independent vertices; Vertex-disjoint cycles 相似文献
2.
In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2nu1 (HSOLSSOM(2nu1)). For u2, necessary conditions for existence of such an HSOLSSOM are that u must be even and n3u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1) n9 and n3u/2+1 or (2) n263 and n2(u-2). In this paper we show that in (1) the condition n9 can be extended to n30 and that in (2), the condition n263 can be improved to n4, except possibly for 19 pairs (n,u), the largest of which is (53,28). 相似文献
3.
Simon J. Smith 《Journal of Approximation Theory》1999,96(2):338
It is shown that the fundamental polynomials for (0, 1, …, 2m+1) Hermite–Fejér interpolation on the zeros of the Chebyshev polynomials of the first kind are non-negative for −1x1, thereby generalising a well-known property of the original Hermite–Fejér interpolation method. As an application of the result, Korovkin's 10theorem on monotone operators is used to present a new proof that the (0, 1, …, 2m+1) Hermite–Fejér interpolation polynomials offC[−1, 1], based onnChebyshev nodes, converge uniformly tofasn→∞. 相似文献
4.
5.
Suppose that G is a graph with n vertices and m edges, and let μ be the spectral radius of its adjacency matrix.Recently we showed that if G has no 4-cycle, then μ2-μn-1, with equality if and only if G is the friendship graph.Here we prove that if m9 and G has no 4-cycle, then μ2m, with equality if G is a star. For 4m8 this assertion fails. 相似文献
6.
Already in his Lectures on Search [A. Rényi, Lectures on the theory of search, University of North Carolina, Chapel Hill, Institute of Statistics, Mimeo Series No. 6007, 1969. [11]] Renyi suggested to consider a search problem, where an unknown is to be found by asking for containment in a minimal number m(n,k) of subsets A1,…,Am with the restrictions |Ai|k<n/2 for i=1,2,…,m.Katona gave in 1966 the lower bound m(n,k)logn/h(k/n) in terms of binary entropy and the upper bound m(n,k)(logn+1)/logn/k·n/k, which was improved by Wegener in 1979 to m(n,k)logn/logn/k(n/k-1).We prove here for k=pn that m(n,k)=logn+o(logn)/h(p), that is, ratewise optimality of the entropy bound: .Actually this work was motivated by a more recent study of Karpovsky, Chakrabarty, Levitin and Avresky of a problem on fault diagnosis in hypercubes, which amounts to finding the minimal number M(n,r) of Hamming balls of radius r=ρn with in the Hamming space , which separate the vertices. Their bounds on M(n,r) are far from being optimal. We establish bounds implyingHowever, it must be emphasized that the methods of prove for our two upper bounds are quite different. 相似文献
7.
Javad Namazi 《Journal of Mathematical Analysis and Applications》2004,290(2):553-562
Let 1<p<∞, and k,m be positive integers such that 0(k−2m)pn. Suppose ΩRn is an open set, and Δ is the Laplacian operator. We will show that there is a sequence of positive constants cj such that for every f in the Sobolev space Wk,p(Ω), for all xΩ except on a set whose Bessel capacity Bk−2m,p is zero. 相似文献
8.
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following:
- 1. , for 1a5, a≠2.
- 2. A8.
- 3. PSL(3,4)e, for 1e10.
- 4. A5×PSL(3,4)e, for 1e10.
- 1. , for 3a5.
- 2. PSL(3,4)e, for 1e10.
9.
There are basic equivalent assertions known for operator monotone functions and operator convex functions in two papers by Hansen and Pedersen. In this note we consider their results as correlation problem between two sequences of matrix n-monotone functions and matrix n-convex functions, and we focus the following three assertions at each label n among them:
- (i) f(0)0 and f is n-convex in [0,α),
- (ii) For each matrix a with its spectrum in [0,α) and a contraction c in the matrix algebra Mn,f(cac)cf(a)c,