{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:32Z","timestamp":1753893812083,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>By $\\delta$ and $w_k$ denote the minimum degree and minimum degree-sum (weight) of a $k$-vertex path in a given graph, respectively.\u00a0For every 3-polytope, $w_2\\le13$ (Kotzig, 1955) and $w_3\\le21$ (Ando, Iwasaki, Kaneko, 1993), where both bounds are sharp. For every 3-polytope with $\\delta\\ge4$, we have sharp bounds $w_2\\le11$ (Lebesgue, 1940) and $w_3\\le17$ (Borodin, 1997).Madaras (2000) proved that every triangulated 3-polytope with $\\delta\\ge4$ satisfies $w_4\\le31$ and constructed such a 3-polytope with $w_4=27$.We improve the Madaras bound $w_4\\le31$ to the sharp bound $w_4\\le27$.<\/jats:p>","DOI":"10.37236\/5602","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:20:08Z","timestamp":1578669608000},"source":"Crossref","is-referenced-by-count":2,"title":["Every Triangulated 3-Polytope of Minimum Degree 4 has a 4-Path of Weight at Most 27"],"prefix":"10.37236","volume":"23","author":[{"given":"O.V.","family":"Borodin","sequence":"first","affiliation":[]},{"given":"A.O.","family":"Ivanova","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,9,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:16:35Z","timestamp":1579220195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5602","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,9,16]]},"article-number":"P3.48"}}