About Supergraphs. Part III

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Summary

The previous articles [5] and [6] introduced formalizations of the step-by-step operations we use to construct finite graphs by hand. That implicitly showed that any finite graph can be constructed from the trivial edgeless graph K1 by applying a finite sequence of these basic operations. In this article that claim is proven explicitly with Mizar[4].

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  • [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics 1(1):107–114 1990.

  • [2] Lowell W. Beineke and Robin J. Wilson editors. Selected Topics in Graph Theory. Academic Press London 1978. ISBN 0-12-086250-6.

  • [3] 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.

  • [4] 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.

  • [5] Sebastian Koch. About supergraphs. Part I. Formalized Mathematics 26(2):101–124 2018. doi:10.2478/forma-2018-0009.

  • [6] Sebastian Koch. About supergraphs. Part II. Formalized Mathematics 26(2):125–140 2018. doi:10.2478/forma-2018-0010.

  • [7] Gilbert Lee and Piotr Rudnicki. Alternative graph structures. Formalized Mathematics 13(2):235–252 2005.

  • [8] Klaus Wagner. Graphentheorie. B.I-Hochschultaschenbücher; 248. Bibliograph. Inst. Mannheim 1970. ISBN 3-411-00248-4.

  • [9] Robin James Wilson. Introduction to Graph Theory. Oliver & Boyd Edinburgh 1972. ISBN 0-05-002534-1.

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