{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:10:41Z","timestamp":1758823841451,"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>A family $\\mathcal{P}$ of subgraphs of $G$ is called a path cover (resp. a path partition) of $G$ if $\\bigcup _{P\\in \\mathcal{P}}V(P)=V(G)$ (resp. $\\dot\\bigcup _{P\\in \\mathcal{P}}V(P)=V(G)$) and every element of $\\mathcal{P}$ is a path. The minimum cardinality of a path cover (resp. a path partition) of $G$ is denoted by ${\\rm pc}(G)$ (resp. ${\\rm pp}(G)$). In this paper, we characterize the forbidden subgraph conditions assuring us that ${\\rm pc}(G)$ (or ${\\rm pp}(G)$) is bounded by a constant. Our main results introduce a new Ramsey-type problem.<\/jats:p>","DOI":"10.37236\/10639","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T01:22:10Z","timestamp":1666056130000},"source":"Crossref","is-referenced-by-count":3,"title":["Ramsey-Type Results for Path Covers and Path Partitions"],"prefix":"10.37236","volume":"29","author":[{"given":"Shuya","family":"Chiba","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michitaka","family":"Furuya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,10,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i4p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i4p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T01:22:10Z","timestamp":1666056130000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i4p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,7]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,10,6]]}},"URL":"https:\/\/doi.org\/10.37236\/10639","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,10,7]]},"article-number":"P4.8"}}