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1.
Let consist of all simple graphs on 2k vertices and edges. For a simple graph G and a positive integer , let denote the number of proper vertex colorings of G in at most colors, and let . We prove that and is the only extremal graph. We also prove that as . © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 135–148, 2007  相似文献   

2.
An old problem of Erd?s, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on vertices, i.e., in a binomial random graph . We prove that with high probability a largest induced regular subgraph of has about vertices. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 235–250, 2011  相似文献   

3.
Let be a k‐uniform hypergraph on n vertices. Suppose that holds for all . We prove that the size of is at most if satisfies and n is sufficiently large. © 2005 Wiley Periodicals, Inc. J Combin Designs  相似文献   

4.
An asymmetric covering is a collection of special subsets S of an n‐set such that every subset T of the n‐set is contained in at least one special S with . In this paper we compute the smallest size of any for We also investigate “continuous” and “banded” versions of the problem. The latter involves the classical covering numbers , and we determine the following new values: , , , , and . We also find the number of non‐isomorphic minimal covering designs in several cases. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 218–228, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10022  相似文献   

5.
We investigate signings of symmetric GDD( , 16, )s over for . Beginning with , at each stage of this process a signing of a GDD( , 16, ) produces a GDD( , 16, ). The initial GDDs ( ) correspond to Hadamard matrices of order 16. For , the GDDs are semibiplanes of order 16, and for the GDDs are semiplanes of order 16 which can be extended to projective planes of order 16. In this article, we completely enumerate such signings which include all generalized Hadamard matrices of order 16. We discuss the generation techniques and properties of the designs obtained during the search. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 119–135, 2009  相似文献   

6.
We consider the special Jin‐Xin relaxation model We assume that the initial data ( ) are sufficiently smooth and close to ( ) in L and have small total variation. Then we prove that there exists a solution ( ) with uniformly small total variation for all t ≥ 0, and this solution depends Lipschitz‐continuously in the L1 norm with respect to time and the initial data. Letting , the solution converges to a unique limit, providing a relaxation limit solution to the quasi‐linear, nonconservative system These limit solutions generate a Lipschitz semigroup on a domain containing the functions with small total variation and close to . This is precisely the Riemann semigroup determined by the unique Riemann solver compatible with (0.1). © 2005 Wiley Periodicals, Inc.  相似文献   

7.
Let be integers, , , and let for each , be a cycle or a tree on vertices. We prove that every graph G of order at least n with contains k vertex disjoint subgraphs , where , if is a tree, and is a cycle with chords incident with a common vertex, if is a cycle. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 87–98, 2009  相似文献   

8.
Let x? be a computed solution to a linear system Ax=b with , where is a proper subclass of matrices in . A structured backward error (SBE) of x? is defined by a measure of the minimal perturbations and such that (1) and that the SBE can be used to distinguish the structured backward stability of the computed solution x?. For simplicity, we may define a partial SBE of x? by a measure of the minimal perturbation such that (2) Can one use the partial SBE to distinguish the structured backward stability of x?? In this note we show that the partial SBE may be much larger than the SBE for certain structured linear systems such as symmetric Toeplitz systems, KKT systems, and dual Vandermonde systems. Besides, certain backward errors for linear least squares are discussed. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

9.
We study the number of n‐vertex graphs that can be written as the edge‐union of k‐vertex cliques. We obtain reasonably tight estimates for in the cases (i) k = n ? o(n) and (ii) k = o(n) but . We also show that exhibits a phase transition around . We leave open several potentially interesting cases, and raise some other questions of a similar nature. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 87–107, 2006  相似文献   

10.
Consider the Emden‐Fowler sublinear dynamic equation (0.1) where $p\in C(\mathbb{T},R)$, where $\mathbb{T}$ is a time scale, 0 < α < 1. When p(t) is allowed to take on negative values, we obtain a Belohorec‐type oscillation theorem for (0.1). As an application, we get that the sublinear difference equation (0.2) is oscillatory, if and the sublinear q‐difference equation (0.3) where $t\in q^{\mathbb{N}_0}, q>1$, is oscillatory, if   相似文献   

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