{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T04:40:19Z","timestamp":1776660019466,"version":"3.51.2"},"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 $[k,n,1]$-graph is a $k$-partite graph with parts of order $n$ such that the bipartite graph induced by any pair of parts is a matching. An independent transversal in such a graph is an independent set that intersects each part in a single vertex. A factor of independent transversals is a set of $n$ pairwise-disjoint independent transversals. Let $f(k)$ be the smallest integer $n_0$ such that every $[k,n,1]$-graph has a factor of independent transversals assuming $n \\geqslant n_0$. Several known conjectures imply that for $k \\geqslant 2$, $f(k)=k$ if $k$ is even and $f(k)=k+1$ if $k$ is odd. While a simple greedy algorithm based on iterating Hall's Theorem shows that $f(k) \\leqslant 2k-2$, no better bound is known and in fact, there are instances showing that the bound $2k-2$ is tight for the greedy algorithm. Here we significantly improve upon the greedy algorithm bound and prove that $f(k) \\leqslant 1.78k$ for all $k$ sufficiently large, answering a question of MacKeigan.<\/jats:p>","DOI":"10.37236\/10529","type":"journal-article","created":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T23:54:04Z","timestamp":1637279644000},"source":"Crossref","is-referenced-by-count":4,"title":["On Factors of Independent Transversals in $k$-Partite Graphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Raphael","family":"Yuster","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,11,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p23\/8446","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p23\/8446","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T23:54:05Z","timestamp":1637279645000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i4p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,19]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10529","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,19]]},"article-number":"P4.23"}}