Volume 9, 1997

University of Bialystok

Copyright (c) 1997 Association of Mizar Users

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

- We prove the Euler theorem on existence of Euler circuits and paths in multigraphs.

This work was partially supported by NSERC Grant OGP9207 and Shinshu Endowment Fund for Information Science.

- Preliminaries
- Degree of a vertex
- Adding an edge to a graph
- Some properties of and operations on cycles
- Euler circuits and paths

- [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.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Czeslaw Bylinski.
A classical first order language.
*Journal of Formalized Mathematics*, 2, 1990. - [9]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [11]
Czeslaw Bylinski and Piotr Rudnicki.
The correspondence between monotonic many sorted signatures and well-founded graphs. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [12]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Krzysztof Hryniewiecki.
Graphs.
*Journal of Formalized Mathematics*, 2, 1990. - [14]
Yatsuka Nakamura and Piotr Rudnicki.
Vertex sequences induced by chains.
*Journal of Formalized Mathematics*, 7, 1995. - [15]
Piotr Rudnicki and Andrzej Trybulec.
Abian's fixed point theorem.
*Journal of Formalized Mathematics*, 9, 1997. - [16]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [17]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [18]
Michal J. Trybulec.
Integers.
*Journal of Formalized Mathematics*, 2, 1990. - [19]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [20]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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