Stability of arc‐transitive graphs

The present paper investigates arc‐transtive graphs in terms of their stability, and shows, somewhat contrary to expectations, that the property of instability is not as rare as previously thought. Until quite recently, the only known example of a finite, arc‐transitive vertex‐determining unstable graph was the underlying graph of the dodecahedron. This paper illustrates some methods for constructing finite arc‐transitive unstable graphs, and three infinite families of such graphs are given as applications. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 95–110, 2001     

On lifted cover inequalities: A new lifting procedure with unusual properties

Lifted cover inequalities are well-known cutting planes for 0–1 linear programs. We show how one of the earliest lifting procedures, due to Balas, can be significantly improved. The resulting procedure has some unusual properties. For example, (i) it can yield facet-defining inequalities even if the given cover is not minimal, (ii) it can yield facet-defining inequalities that cannot be obtained by standard lifting procedures, and (iii) the associated superadditive lifting function is integer-valued almost everywhere.     

$f$-投射与$f$-内射模

Let R be a ring. A fight R-module M is called f-projective if Ext^1 （M, N） = 0 for any f-injective right R-module N. We prove that （F-proj,F-inj） is a complete cotorsion theory, where （F-proj （F-inj） denotes the class of all f-projective （f-injective） right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules.     

Graphs of arbitrary excessive class

We show that there exists a family of r-regular graphs of arbitrarily large excessive index for each integer r greater than 3. Furthermore, we answer a question in Bonisoli and Cariolaro (2007) [1] showing that all the positive integers can be attained as excessive classes of regular graphs.     

On Generating Random Intervals and Hyperrectangles

Abstract

We look at the problem of generating a random hyperrectangle in a unit hypercube such that each point of the hypercube has probability p of being covered. For random intervals of [0, 1], we compare various methods based either on the distribution of the length or on the distribution of the midpoint. It is shown that no constant length solution exists. Nice versatility is achieved when a random interval is chosen from among the spacings defined by a Dirichlet process. A small simulation is included.     

Note on cycle double covers of graphs

Kriesell [M. Kriesell, Contractions, cycle double covers and cyclic colorings in locally connected graphs, J. Combin. Theory Ser. B 96 (2006) 881-900] proved the cycle double cover conjecture for locally connected graphs. In this note, we give much shorter proofs for two stronger results.     

Graphs with Cayley canonical double covers

A canonical double cover $B\left(X\right)$ of a graph $X$ is the direct product of $X$ and the complete graph $K_2$ on two vertices. In order to answer the question when a canonical double cover of a given graph is a Cayley graph, in 1992 Maru?i? et al. introduced the concept of generalized Cayley graphs. In this paper this concept is generalized to a wider class of graphs, the so-called extended generalized Cayley graphs. It is proved that the canonical double cover of a connected non-bipartite graph $X$ is a Cayley graph if and only if $X$ is an extended generalized Cayley graph. This corrects an incorrectly stated claim in [Discrete Math. 102 (1992), 279–285].     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.     

The generalized approximate Perron integral

In this paper we introduce the concept of the generalized AP-integral and discuss the properties of this integral.      

On Cubic Bridgeless Graphs Whose Edge‐Set Cannot be Covered by Four Perfect Matchings

The problem of establishing the number of perfect matchings necessary to cover the edge‐set of a cubic bridgeless graph is strictly related to a famous conjecture of Berge and Fulkerson. In this article, we prove that deciding whether this number is at most four for a given cubic bridgeless graph is NP‐complete. We also construct an infinite family of snarks (cyclically 4‐edge‐connected cubic graphs of girth at least 5 and chromatic index 4) whose edge‐set cannot be covered by four perfect matchings. Only two such graphs were known. It turns out that the family also has interesting properties with respect to the shortest cycle cover problem. The shortest cycle cover of any cubic bridgeless graph with m edges has length at least , and we show that this inequality is strict for graphs of . We also construct the first known snark with no cycle cover of length less than .