Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

## The Class of Series-Parallel Graphs. Part II

Krzysztof Retel
University of Bialystok

### Summary.

In this paper we introduce two new operations on graphs: sum and union corresponding to parallel and series operation respectively. We determine $N$-free graph as the graph that does not embed Necklace $4$. We define fin\_RelStr" as the set of all graphs with finite carriers. We also define the smallest class of graphs which contains the one-element graph and which is closed under parallel and series operations. The goal of the article is to prove the theorem that the class of finite series-parallel graphs is the class of finite $N$-free graphs. This paper formalizes the next part of [12].

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.

#### MML Identifier: NECKLA_2

The terminology and notation used in this paper have been introduced in the following articles [14] [13] [18] [7] [20] [8] [1] [2] [3] [15] [17] [4] [16] [19] [11] [5] [6] [9] [10]

Contents (PDF format)

#### Bibliography

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