{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810994,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The detour order of a graph $G$, denoted by $\\tau \\left( G\\right) ,$ is the order of a longest path in $G.$ A partition of the vertex set of $G$ into two sets, $A$ and $B,$ such that $\\tau (\\left\\langle A\\right\\rangle )\\leq a$ and $\\tau (\\left\\langle B\\right\\rangle )\\leq b$ is called an $(a,b)$-partition of $G$. If $G$ has an $(a,b)$-partition for every pair $(a,b)$ of positive integers such that $a+b=\\tau (G),$ then we say that $G$ is $\\tau $-partitionable. The Path Partition Conjecture (PPC), which was discussed by Lov\u00e1sz and Mih\u00f3k in 1981 in Szeged, is that every graph is $\\tau $-partitionable. It is known that a graph $G$ of order $n$ and detour order $\\tau =n-p$ is $\\tau $-partitionable if $p=0,1.$ We show that this is also true for $p=2,3,$ and for all $p\\geq 4$ provided that $n\\geq p(10p-3).$<\/jats:p>","DOI":"10.37236\/1945","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:09:31Z","timestamp":1578719371000},"source":"Crossref","is-referenced-by-count":4,"title":["An Asymptotic Result for the Path Partition Conjecture"],"prefix":"10.37236","volume":"12","author":[{"given":"Marietjie","family":"Frick","sequence":"first","affiliation":[]},{"given":"Ingo","family":"Schiermeyer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,9,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:50Z","timestamp":1579322450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1945","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,9,29]]},"article-number":"R48"}}