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We characterize the graphs whose associated matching polytopes are Gorenstein, and then prove that all Gorenstein matching polytopes possess the integer decomposition property. As a special case study, we examine the matching polytopes of wheel graphs and show that they are <jats:italic>not<\/jats:italic> Gorenstein, but <jats:italic>do<\/jats:italic> possess the integer decomposition property.<\/jats:p>","DOI":"10.1007\/s00373-025-02923-8","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T13:23:24Z","timestamp":1744809804000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Matching Polytopes, Gorensteinness, and the Integer Decomposition Property"],"prefix":"10.1007","volume":"41","author":[{"given":"Benjamin","family":"Eisley","sequence":"first","affiliation":[]},{"given":"Koji","family":"Matsushita","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7437-3745","authenticated-orcid":false,"given":"Andr\u00e9s R.","family":"Vindas-Mel\u00e9ndez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,16]]},"reference":[{"key":"2923_CR1","unstructured":"Adiprasito, K.A., Papadakis, S.A., Petrotou, V., Steinmeyer, J.K.: Beyond positivity in Ehrhart theory. 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