Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Oriented Chains


Yatsuka Nakamura
Shinshu University, Nagano
Piotr Rudnicki
University of Alberta, Edmonton

Summary.

In [8] we introduced a number of notions about vertex sequences associated with undirected chains of edges in graphs. In this article, we introduce analogous concepts for oriented chains and use them to prove properties of cutting and glueing of oriented chains, and the existence of a simple oriented chain in an oriented chain.

MML Identifier: GRAPH_4

The terminology and notation used in this paper have been introduced in the following articles [10] [12] [13] [4] [3] [5] [11] [1] [6] [2] [7] [8] [9]

Contents (PDF format)

  1. Oriented Vertex Sequences
  2. Cutting and Glueing of Oriented Chains
  3. Oriented Simple Chains in Oriented Chains

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[6] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[7] Krzysztof Hryniewiecki. Graphs. Journal of Formalized Mathematics, 2, 1990.
[8] Yatsuka Nakamura and Piotr Rudnicki. Vertex sequences induced by chains. Journal of Formalized Mathematics, 7, 1995.
[9] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[10] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[11] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[13] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received August 19, 1998


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