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A polynomial algorithm for minDSC on a subclass of series Parallel graphs

Salim Achouri, Timothée Bossart, Alix Munier-Kordon (2009)

RAIRO - Operations Research

The aim of this paper is to show a polynomial algorithm for the problem minimum directed sumcut for a class of series parallel digraphs. The method uses the recursive structure of parallel compositions in order to define a dominating set of orders. Then, the optimal order is easily reached by minimizing the directed sumcut. It is also shown that this approach cannot be applied in two more general classes of series parallel digraphs.

A Poster about the Old History of Fractional Calculus

Tenreiro Machado, J., Kiryakova, Virginia, Mainardi, Francesco (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.

A prime factor theorem for a generalized direct product

Wilfried Imrich, Peter F. Stadler (2006)

Discussiones Mathematicae Graph Theory

We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.

A proof of menger's theorem by contraction

Frank Göring (2002)

Discussiones Mathematicae Graph Theory

A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.

A proof of the crossing number of K 3 , n in a surface

Pak Tung Ho (2007)

Discussiones Mathematicae Graph Theory

In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of K 3 , n in a surface with Euler genus ε is ⎣n/(2ε+2)⎦ n - (ε+1)(1+⎣n/(2ε+2)⎦).

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