{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T13:57:42Z","timestamp":1715695062497},"reference-count":4,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T00:00:00Z","timestamp":1651622400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T00:00:00Z","timestamp":1651622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"ELKH Alfr\u00e9d R\u00e9nyi Institute of Mathematics"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We determine the maximum number of edges in a <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>K<\/mml:mi>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-minor-free <jats:italic>n<\/jats:italic>-vertex graph of girth <jats:italic>g<\/jats:italic>, when <jats:inline-formula><jats:alternatives><jats:tex-math>$$g=5$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>g<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>5<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> or <jats:italic>g<\/jats:italic> is even. We argue that there are many different <jats:italic>n<\/jats:italic>-vertex extremal graphs if <jats:italic>n<\/jats:italic> is even and <jats:italic>g<\/jats:italic> is odd.<\/jats:p>","DOI":"10.1007\/s10998-022-00465-7","type":"journal-article","created":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T14:02:49Z","timestamp":1651672969000},"page":"108-114","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Extremal $$K_4$$-minor-free graphs without short cycles"],"prefix":"10.1007","volume":"86","author":[{"given":"J\u00e1nos","family":"Bar\u00e1t","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,4]]},"reference":[{"key":"465_CR1","unstructured":"J\u00e1nos Bar\u00e1t. On the number of edges in a $$K_5$$-minor-free graph of given girth. submitted"},{"key":"465_CR2","volume-title":"Graph theory vol. 244 of graduate texts in mathematics","author":"J Adrian Bondy","year":"2008","unstructured":"J. Adrian Bondy, U.S. Ram Murty, Graph theory vol. 244 of graduate texts in mathematics (Springer, New York, 2008)"},{"key":"465_CR3","volume-title":"Graph theory, vol. 163 of graduate texts in mathematics","author":"D Reinhard","year":"2016","unstructured":"D. Reinhard, Graph theory, vol. 163 of graduate texts in mathematics, 5th edn. (Springer, New York, 2016)","edition":"5"},{"key":"465_CR4","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1002\/jgt.3190070205","volume":"7","author":"T Carsten","year":"1983","unstructured":"T. Carsten, A theorem on paths in planar graphs. J. Gr. Theory 7, 169\u2013176 (1983)","journal-title":"J. Gr. Theory"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-022-00465-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-022-00465-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-022-00465-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T15:30:06Z","timestamp":1677511806000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-022-00465-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,4]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["465"],"URL":"https:\/\/doi.org\/10.1007\/s10998-022-00465-7","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,4]]},"assertion":[{"value":"11 October 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}