Note on Enomoto and Ota’s Conjecture for Short Paths in Large Graphs

With sufficient minimum degree sum, Enomoto and Ota conjectured that for any selected set of vertices, there exists a spanning collection of disjoint paths, each starting at one of the selected vertices and each having a prescribed length. Using the Regularity Lemma, we prove that this claim holds without the spanning assumption if the vertex set of the host graph is sufficiently large.     

Properly colored paths and cycles

In an edge-colored graph, let d^c(v) be the number of colors on the edges incident to v and let δ^c(G) be the minimum d^c(v) over all vertices v∈G. In this work, we consider sharp conditions on δ^c(G) which imply the existence of properly edge-colored paths and cycles, meaning no two consecutive edges have the same color.     

承诺方案的研究

承诺方案是一种重要而有用的密码学基本协议,它在密码学领域中的零知识证明、安全多方计算协议、电子货币、电子选举等众多密码学协议的构造中起着十分重要的作用.我们介绍了承诺方案的应用背景、定义、分类、构造以及它在密码学领域中所起的重要作用.同时,对目前密码学领域中关于承诺方案的研究热点也进行了阐述.     

Pan-H-Linked Graphs

Let H be a multigraph, possibly containing loops. An H-subdivision is any simple graph obtained by replacing the edges of H with paths of arbitrary length. Let H be an arbitrary multigraph of order k, size m, n ₀(H) isolated vertices and n ₁(H) vertices of degree one. In Gould and Whalen (Graphs Comb. 23:165–182, 2007) it was shown that if G is a simple graph of order n containing an H-subdivision H{\mathcal{H}} and d(G) 3 \fracn+m-k+n₁(H)+2n₀(H)2{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}}, then G contains a spanning H-subdivision with the same ground set as H{\mathcal{H}} . As a corollary to this result, the authors were able to obtain Dirac’s famed theorem on hamiltonian graphs; namely that if G is a graph of order n ≥ 3 with d(G) 3 \fracn2{\delta(G)\ge\frac{n}{2}} , then G is hamiltonian. Bondy (J. Comb. Theory Ser. B 11:80–84, 1971) extended Dirac’s theorem by showing that if G satisfied the condition d(G) 3 \fracn2{\delta(G) \ge \frac{n}{2}} then G was either pancyclic or a complete bipartite graph. In this paper, we extend the result from Gould and Whalen (Graphs Comb. 23:165–182, 2007) in a similar manner. An H-subdivision H{\mathcal{H}} in G is 1-extendible if there exists an H-subdivision H^*{\mathcal{H}^{*}} with the same ground set as H{\mathcal{H}} and |H^*| = |H| + 1{|\mathcal{H}^{*}| = |\mathcal{H}| + 1} . If every H-subdivision in G is 1-extendible, then G is pan-H-linked. We demonstrate that if H is sufficiently dense and G is a graph of large enough order n such that d(G) 3 \fracn+m-k+n₁(H)+2n₀(H)2{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}} , then G is pan-H-linked. This result is sharp.     

一类单圈T函数的判定

多项式函数作为一类密码学中常用的T-函数,其可逆性、周期性一直是相关研究中的重要问题.借助于2-adic整数的乘法公式,给出了T-函数p(x)=a0⊕a1x⊕…⊕adxd(mod2n)是单圈函数的充要条件.     

基于吴方法判断代数集上多项式自同态是否为同构

给出仿射代数集上多项式自同态为同构的Ｇｒｏｂｎｅｒ基准则,井利用Ｗｕ－Ｒｉｔｔ算法进行了计算,同时给出一些具体例子．     

Extensions of Gallai–Ramsey results

Consider the graph consisting of a triangle with a pendant edge. We describe the structure of rainbow ‐free edge colorings of a complete graph and provide some corresponding Gallai–Ramsey results. In particular, we extend a result of Gallai to find a partition of the vertices of a rainbow ‐free colored complete graph with a limited number of colors between the parts. We also extend some Gallai–Ramsey results of Chung and Graham, Faudree et al. and Gyárfás et al. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory     

关于多项式映射自同构恒等集的一个注记

本文给出了判定一个仿射代数集是否是一个自同构恒等集的充分条件.作为一个推论,我们给出了Mckay-Wang的一个问题的一个新证明.我们也给出了一些具体的例子来说明主要的定理.