On Arc-Regular Permutation Groups Using Latin Squares

For a given a permutation group G, the problem of determining which regular digraphs admit G as an arc-regular group of automorphism is considered. Groups which admit such a representation can be characterized in terms of generating sets satisfying certain properties, and a procedure to manufacture such groups is presented. The technique is based on constructing appropriate factorizations of (smaller) regular line digraphs by means of Latin squares. Using this approach, all possible representations of transitive groups of degree up to seven as arc-regular groups of digraphs of some degree is presented.Partially supported by the Comissionat per a Universitats i Recerca of the Generalitat de Catalunya under Grant 1997FI-693, and through a European Community Marie Curie Fellowship under contract HPMF-CT-2001-01211.     

Pathwidth of Planar and Line Graphs

 We prove that for every 2-connected planar graph the pathwidth of its geometric dual is less than the pathwidth of its line graph. This implies that pathwidth(H)≤ pathwidth(H ^*)+1 for every planar triangulation H and leads us to a conjecture that pathwidth(G)≤pathwidth(G ^*)+1 for every 2-connected graph G. Received: May 8, 2001 Final version received: March 26, 2002 RID="*" ID="*" I acknowledge support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies) and support by the RFBR grant N01-01-00235. Acknowledgments. I am grateful to Petr Golovach, Roland Opfer and anonymous referee for their useful comments and suggestions.     

具有四个时滞的平面系统的周期解的存在性

The sufficient condition for the existence of non-constant periodic solutions of the following planar system with four delays are obtained:     

ON ARC-TRANSITIVE CIRCULANT DIGRAPHS

Denote by c,(s)the circulant digraph with vertex set zn=[0,1,2……n-1]and symbol set s(≠-s)∈zn\[0].let x be the automorphism group of cn(S)and xo the stabilizer of o in x.then cn(S)is arctransitive if and only if xo acts transitively on s.in this paper,co(S)with xo is being the symmetric group is characterized by its symbot set .by the way all the arctransitive clcculant digraphs of degree 2are given.     

A Randomized Parallel Algorithm for Planar Graph Isomorphism

We present a parallel randomized algorithm running on aCRCW PRAM, to determine whether two planar graphs are isomorphic, and if so to find the isomorphism. We assume that we have a tree of separators for each planar graph (which can be computed by known algorithms inO(log² n) time withn^{1 + ε}processors, for any ε > 0). Ifnis the number of vertices, our algorithm takesO(log(n)) time with processors and with a probability of failure of 1/nat most. The algorithm needs 2 · log(m) − log(n) + O(log(n)) random bits. The number of random bits can be decreased toO(log(n)) by increasing the number of processors ton^{3/2 + ε}, for any ε > 0. Our parallel algorithm has significantly improved processor efficiency, compared to the previous logarithmic time parallel algorithm of Miller and Reif (Siam J. Comput.20(1991), 1128–1147), which requiresn⁴randomized processors orn⁵deterministic processors.     

Revisit the Lovász Local Lemma

We provide a sufficient condition for showing that the probability of none of the events A ₁, A ₂,...,A _n occurs is positive. This condition explicitly involves the dependency digraph and the probabilities of the A _i's. Some applications are given.     

n连通,k临界有向图的性质

本文研究了n连通、k临界有向图的一些性质,主要结论:每一个临界强连通有向图至少有两个顶点出度为一,同时也至少有两个与之不同的顶点入度为一。本结论加强了[1]中所得到的结论,并用完全不同于[1]的方法证明了对n≥2不存在非完全的n连通、n临界有向图。     

循环图Adam同构类的计数（Ⅱ）

文[1]讨论了无向循环图Adam同构磁的计数,本文继续讨论有向循环图Adam同构类的计数问题,对于有向循环图类,且,且是奇素数}以及都是素数}分别给出了Adam同构类的计数公式。     

布尔矩阵的组合合成及其图表示

本文综术了有关布尔矩阵的组合合成的现有结果,用图论方法展示了它们的组合性质,提出了一些待解决的问题。     

ISOMORPHISMS OF CIRCULANT DIAGAPHS

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