Linear arboricity of regular digraphs

A linear directed forest is a directed graph in which every component is a directed path.The linear arboricity la(D) of a digraph D is the minimum number of linear directed forests in D whose union covers all arcs of D. For every d-regular digraph D, Nakayama and P′eroche conjecture that la(D) = d + 1. In this paper, we consider the linear arboricity for complete symmetric digraphs,regular digraphs with high directed girth and random regular digraphs and we improve some wellknown results. Moreover, we propose a more precise conjecture about the linear arboricity for regular digraphs.     

Platonic surfaces

If S _O is a Riemann surface with a complete metric of finite area and constant curvature -1, let S _C denote the conformal compactification of S _O. We show that, under the assumption that the cusps of S _O are large, there is a close relationship between the hyperbolic metrics on S _O and S _C. We use this relationship to show that , where the Platonic surface P _k is the conformal compactification of the modular surface S _k. Received: November, 1996; revised: February, 1998     

序Banach空间中不连续增算子的不动点

本文在较弱的紧性条件下,给出了序Banach空间中不连续增算子的不动点的存在性结果．     

Dickson’s Lemma,Higman’s Theorem and Beyond: A survey of some basic results in order theory

We provide proofs for the fact that certain orders have no infinite descending chains and no infinite antichains.     

Another proof of the kuhn-tucker theorem ∗

A proof of the Kuhn-Tucker theorem is given using Zorn's Lemma     

Levi's Lemma,pseudolinear drawings of,and empty triangles

There are three main thrusts to this article: a new proof of Levi's Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudolinear drawings of the complete graph; and proofs that pseudolinear and convex drawings of have O and O(n²), respectively, empty triangles. All the arguments are elementary, algorithmic, and self‐contained.     

Infinitely many solutions for non-autonomous second-order systems with impulsive effects

In this paper, we establish the existence of infinitely many solutions for a class of non-autonomous second-order systems with impulsive effects. Our technique is based on the Fountain Theorem of Bartsch and the Symmetric Mountain Pass Lemma due to Kajikiya.     

图的邻点可区别VE-全色数的一个上界

根据图的邻点可区别VE-全染色的定义和性质,用概率方法研究了图的邻点可区别VE-全染色,并给出了图的邻点可区别VE-全色数的一个上界.如果δ≥7且△≥25,则有x_at^ue（G）≤7△,其中δ是图G的最小度,△是图G的最大度.