Introduction to Graph Enumerations

Sebastian Koch

doi:10.2478/forma-2023-0004

.blurhash-client-img { display: none !important; }

Introduction to Graph Enumerations

Formalized Mathematics

Volume 31 (2023): Issue 1 (September 2023)

By: Sebastian Koch

Open Access

|Sep 2023

Abstract

In this article sets of certain subgraphs of a graph are formalized in the Mizar system [7], [1], based on the formalization of graphs in [11] briefly sketched in [12]. The main result is the spanning subgraph theorem.

References

Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.
Search in Google Scholar Back to article
John Adrian Bondy and U. S. R. Murty. Graph Theory. Graduate Texts in Mathematics, 244. Springer, New York, 2008. ISBN 978-1-84628-969-9.
Search in Google Scholar Back to article
Ricky W. Butler and Jon A. Sjogren. A PVS graph theory library. Technical report, NASA Langley, 1998.
Search in Google Scholar Back to article
Ching-Tsun Chou. A formal theory of undirected graphs in higher-order logic. In Thomas F. Melham and Juanito Camilleri, editors, Higher Order Logic Theorem Proving and Its Applications, 7th International Workshop, Valletta, Malta, September 19–22, 1994, Proceedings, volume 859 of Lecture Notes in Computer Science, pages 144–157. Springer, 1994. doi:10.1007/3-540-58450-1 40.
Search in Google Scholar Back to article
Reinhard Diestel. Graph Theory, volume Graduate Texts in Mathematics; 173. Springer, Berlin, fifth edition, 2017. ISBN 978-3-662-53621-6.
Search in Google Scholar Back to article
Jessica Enright and Piotr Rudnicki. Helly property for subtrees. Formalized Mathematics, 16(2):91–96, 2008. doi:10.2478/v10037-008-0013-3.
Search in Google Scholar Back to article
Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.
Search in Google Scholar Back to article
Sebastian Koch. Miscellaneous graph preliminaries. Part I. Formalized Mathematics, 29 (1):21–38, 2021. doi:10.2478/forma-2021-0003.
Search in Google Scholar Back to article
Sebastian Koch. Underlying simple graphs. Formalized Mathematics, 27(3):237–259, 2019. doi:10.2478/forma-2019-0023.
Search in Google Scholar Back to article
Sebastian Koch. About graph sums. Formalized Mathematics, 29(4):249–278, 2021. doi:10.2478/forma-2021-0023.
Search in Google Scholar Back to article
Gilbert Lee and Piotr Rudnicki. Alternative graph structures. Formalized Mathematics, 13(2):235–252, 2005.
Search in Google Scholar Back to article
Gilbert Lee and Piotr Rudnicki. Alternative aggregates in Mizar. In Manuel Kauers, Manfred Kerber, Robert Miner, and Wolfgang Windsteiger, editors, Towards Mechanized Mathematical Assistants, pages 327–341, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. ISBN 978-3-540-73086-6. doi:10.1007/978-3-540-73086-6 26.
Search in Google Scholar Back to article
Lars Noschinski. A graph library for Isabelle. Mathematics in Computer Science, 9(1): 23–39, 2015. doi:10.1007/s11786-014-0183-z.
Search in Google Scholar Back to article
Robin James Wilson. Introduction to Graph Theory. Oliver & Boyd, Edinburgh, 1972. ISBN 0-05-002534-1.
Search in Google Scholar Back to article