$K_v$到$P_3$和$K_3$图的一致可分解

可分解h-sun设计

Resolvable h-sun designs

本文完全确定了完全图K_v到r ~ 1-因子和s类的一致可分解的谱。

除一个块外所有块大小为2的类均匀可分解设计

Class-uniformly resolvable designs with all but one block having size two

研究每个平行类包含一个大小为m的块、其余块大小为2的类均匀可分解设计，给出存在性的必要条件及两种构造方法。

$K_v$ 的均匀可分解分解为 $1$-因子和奇数 $n$-星因子

Uniformly resolvable decompositions of $K_v$ into $1$-factors and odd $n$-star factors

研究完全图 $K_v$ 的均匀可分解分解，其中每个分解类由 $K_2$ 或奇数 $n$-星 $K_{1,n}$ 组成，并给出部分解。

当 $n>1$ 为奇数时，$K_v$ 关于一个 $1$-因子和 $n$-星的均匀可分解分解

Uniformly resolvable decompositions of $K_v$ into one $1$-factor and $n$-stars when $n>1$ is odd

本文研究了完全图 $K_v$ 的均匀可分解分解，其中一类为 $K_2$，其余为 $K_{1,n}$（$n>1$ 为奇数），并给出了完整解。

Almost all Steiner triple systems are almost resolvable

We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).

可分辨的三星设计

Resolvable 3-star designs

设Kv是v阶完全图，F是Kv的1-因子集.本文研究了当F具有最小1-因子数时Kv-F的可分解为3-星的存在性。我们完全解决了F具有最小数量的1-因子的情况，除了{40，44，52，76，92，100，280，284，328，332，428，472，476，572}中的v可能例外。

关于等圈长的有向Oberwolfach问题：奇情况

On the directed Oberwolfach Problem with equal cycle lengths: the odd case

证明了完全对称有向图$K_{2m}^\ast$对所有奇数$m$，$5 \le m \le 49$都可分解为长度为$m$的有向圈.因此，$K_{n}^\ast$允许对所有$n \equiv 0 \pmod{2m}$和奇数$m$，$5 \le m \le 49$，可分解为长度为$m$的有向圈。

Graph decompositions in projective geometries

Let PG$(\mathbb{F}_q^v)$ be the $(v-1)$-dimensional projective space over $\mathbb{F}_q$ and let $Γ$ be a simple graph of order ${q^k-1\over q-1}$ for some $k$. A 2$-(v,Γ,λ)$ design over $\mathbb{F}_q$ is a collection $\cal B$ of graphs (\textit{blocks}) isomorphic to $Γ$ with the following properties: the vertex set of every block is a subspace of PG$(\mathbb{F}_q^v)$; every two distinct points of PG$(\mathbb{F}_q^v)$ are adjacent in exactly $λ$ blocks. This new definition covers, in particular, the well known concept of a 2$-(v,k,λ)$ design over $\mathbb{F}_q$ corresponding to the case that …

A bandwidth theorem for approximate decompositions

We provide a degree condition on a regular $n$-vertex graph $G$ which ensures the existence of a near optimal packing of any family $\mathcal H$ of bounded degree $n$-vertex $k$-chromatic separable graphs into $G$. In general, this degree condition is best possible. Here a graph is separable if it has a sublinear separator whose removal results in a set of components of sublinear size. Equivalently, the separability condition can be replaced by that of having small bandwidth. Thus our result can be viewed as a version of the bandwidth theorem of Böttcher, Schacht and Taraz in the setting of ap…

Stein方法、周期分布和对称群中最长元的约化分解

Stein's method, semicircle distribution, and reduced decompositions of the longest element in the symmetric group

考虑对称群中最长元的一致随机约化分解。已知在该分解中第一转置的位置收敛于周期分布。在本文中，我们使用Stein方法的“生成元比较”方法，为这个结果提供了一个尖锐的误差项。

Track Layouts, Layered Path Decompositions, and Leveled Planarity

We investigate two types of graph layouts, track layouts and layered path decompositions, and the relations between their associated parameters track-number and layered pathwidth. We use these two types of layouts to characterize leveled planar graphs, which are the graphs with planar leveled drawings with no dummy vertices. It follows from the known NP-completeness of leveled planarity that track-number and layered pathwidth are also NP-complete, even for the smallest constant parameter values that make these parameters nontrivial. We prove that the graphs with bounded layered pathwidth inclu…

虚 torsion 自由和虚自由群的组合特征

Combinatorial Characterizations of Virtually Torsion-Free and Virtually Free Groups

本文通过图分解理论，研究了虚 torsion 自由和虚自由群的组合特征，并建立了相应的等价条件。

关于随机有向无环图的 Markov 等价类的数量与大小

On the number and size of Markov equivalence classes of random directed acyclic graphs

本文研究了均匀随机有向无环图的 Markov 等价类，利用塔分解证明了等价类与图的比值趋于正常数，且典型等价类大小有界并具有超多项式尾部。

正则平面图的Schnyder分解及其在作图中的应用

Schnyder decompositions for regular plane graphs and application to drawing

Schnyder森林是将简单三角剖分分解为三个边不相交的生成树，它们以特定的方式相互交叉。在这篇文章中，我们定义了一个推广的Schnyder木材$d$ -角（平面图与度$d$的面）为所有$d\geq 3$。\emph{Schnyder decomposition}是一组以特定方式彼此交叉的$d$生成林，并且使得每个内部边缘恰好是生成林的$d-2$的一部分。我们表明，Schnyder分解存在当且仅当周长的$d$角是$d$。与Schnyder woods（$d=3$）的情况一样，在取向（当使用$d\geq 5$时为“分数”取向）和角标记方面也有替代的公式。此外，在固定的$d$ -围长$d$的角上的Schnyder分解的集合是分配格。我们还表明，Schnyder分解（$d$ -经常平面图的mincut $d$植根于顶点$v^*$）的结构对偶分解成$d$生成树植根于$v^*$，使每个边不事件$v^*$是在相反的方向使用的两棵树。此外，甚至值的$d$，我们表明，一个子类的Schnyder分解，这是所谓的甚至，享受额外的属性，产生一个减少制定;在d=4的情况下，这些对应于简单的四边形结构（2-方向和分区成2个生成树）研究。在d=4的情况下，偶Schnyder分解的对偶产生（平面）正交和直线绘制算法。对于一个4-正则平面图$G$，其顶点为$n$，加上一个标记顶点$v$，$G\backslash …