{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:26:15Z","timestamp":1759335975169,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Hladk\u00fd, Hu, and Piguet [Tilings in graphons, preprint] introduced the notions of matching and fractional vertex covers in graphons. These are counterparts to the corresponding notions in finite graphs.\u00a0\r\nCombinatorial optimization studies the structure of the matching polytope and the fractional vertex cover polytope of a graph. Here, in analogy, we initiate the study of the structure of the set of all matchings and of all fractional vertex covers in a graphon. We call these sets the matching polyton and the fractional vertex cover polyton.\r\nWe also study properties of matching polytons and fractional vertex cover polytons along convergent sequences of graphons.\r\n\u00a0As an auxiliary tool of independent interest, we prove that a graphon is $r$-partite if and only if it contains no graph of chromatic number $r+1$. This in turn gives a characterization of bipartite graphons as those having a symmetric spectrum.<\/jats:p>","DOI":"10.37236\/6241","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:02:11Z","timestamp":1578636131000},"source":"Crossref","is-referenced-by-count":3,"title":["Matching Polytons"],"prefix":"10.37236","volume":"26","author":[{"given":"Martin","family":"Dole\u017eal","sequence":"first","affiliation":[]},{"given":"Jan","family":"Hladk\u00fd","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p38\/7963","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p38\/7963","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:01:31Z","timestamp":1579233691000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,22]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/6241","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,11,22]]},"article-number":"P4.38"}}