{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T02:05:59Z","timestamp":1783908359222,"version":"3.55.0"},"reference-count":9,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,4,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library to the best of the author\u2019s knowledge. Most of them regard graph theory as formalized in the GLIB series and are needed in upcoming articles.<\/jats:p>","DOI":"10.2478\/forma-2021-0003","type":"journal-article","created":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T11:48:51Z","timestamp":1630064931000},"page":"21-38","source":"Crossref","is-referenced-by-count":3,"title":["Miscellaneous Graph Preliminaries. Part I"],"prefix":"10.2478","volume":"29","author":[{"given":"Sebastian","family":"Koch","sequence":"first","affiliation":[{"name":"Johannes Gutenberg University Mainz , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2021,8,26]]},"reference":[{"key":"2026071212491074620_j_forma-2021-0003_ref_001","doi-asserted-by":"crossref","unstructured":"[1] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.10.1007\/s10817-017-9440-6604425130069070","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026071212491074620_j_forma-2021-0003_ref_002","unstructured":"[2] 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."},{"key":"2026071212491074620_j_forma-2021-0003_ref_003","unstructured":"[3] Pavol Hell and Jaroslav Nesetril. Graphs and homomorphisms. Oxford Lecture Series in Mathematics and Its Applications; 28. Oxford University Press, Oxford, 2004. ISBN 0-19-852817-5."},{"key":"2026071212491074620_j_forma-2021-0003_ref_004","doi-asserted-by":"crossref","unstructured":"[4] Ulrich Knauer. Algebraic graph theory: morphisms, monoids and matrices, volume 41 of De Gruyter Studies in Mathematics. Walter de Gruyter, 2011.10.1515\/9783110255096","DOI":"10.1515\/9783110255096"},{"key":"2026071212491074620_j_forma-2021-0003_ref_005","doi-asserted-by":"crossref","unstructured":"[5] Sebastian Koch. Miscellaneous graph preliminaries. Formalized Mathematics, 28(1):23\u201339, 2020. doi:10.2478\/forma-2020-0003.10.2478\/forma-2020-0003","DOI":"10.2478\/forma-2020-0003"},{"key":"2026071212491074620_j_forma-2021-0003_ref_006","doi-asserted-by":"crossref","unstructured":"[6] Sebastian Koch. About supergraphs. Part I. Formalized Mathematics, 26(2):101\u2013124, 2018. doi:10.2478\/forma-2018-0009.10.2478\/forma-2018-0009","DOI":"10.2478\/forma-2018-0009"},{"key":"2026071212491074620_j_forma-2021-0003_ref_007","doi-asserted-by":"crossref","unstructured":"[7] Sebastian Koch. About graph mappings. Formalized Mathematics, 27(3):261\u2013301, 2019. doi:10.2478\/forma-2019-0024.10.2478\/forma-2019-0024","DOI":"10.2478\/forma-2019-0024"},{"key":"2026071212491074620_j_forma-2021-0003_ref_008","unstructured":"[8] Gilbert Lee and Piotr Rudnicki. Alternative graph structures. Formalized Mathematics, 13(2):235\u2013252, 2005."},{"key":"2026071212491074620_j_forma-2021-0003_ref_009","unstructured":"[9] Robin James Wilson. Introduction to Graph Theory. Oliver & Boyd, Edinburgh, 1972. ISBN 0-05-002534-1."}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2021-0003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T01:10:16Z","timestamp":1783905016000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2021-0003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,1]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,8,26]]},"published-print":{"date-parts":[[2021,4,1]]}},"alternative-id":["10.2478\/forma-2021-0003"],"URL":"https:\/\/doi.org\/10.2478\/forma-2021-0003","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,1]]}}}