{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:03Z","timestamp":1753893843359,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A $(k_1+k_2)$-bispindle\u00a0is the union of $k_1$ $(x,y)$-dipaths and $k_2$ $(y,x)$-dipaths, all these dipaths being pairwise internally disjoint.\u00a0Recently, Cohen et al. showed that for every $(1,1)$- bispindle $B$, there exists an integer $k$ such that every strongly connected\u00a0digraph with chromatic number greater than $k$ contains a subdivision of $B$. We investigate generalizations of\u00a0this result by first showing constructions of strongly connected digraphs with large chromatic number without any $(3,0)$-bispindle\u00a0or $(2,2)$-bispindle. We then consider $(2,1)$-bispindles. Let $B(k_1,k_2;k_3)$ denote the $(2,1)$-bispindle formed by three internally disjoint dipaths between two vertices $x,y$,\u00a0two $(x,y)$-dipaths, one of length $k_1$ and the other of length $k_2$, and one $(y,x)$-dipath of length $k_3$. We conjecture that for any positive integers $k_1, k_2,k_3$, there is an integer $g(k_1,k_2,k_3)$ such that every strongly connected\u00a0digraph with chromatic number greater than $g(k_1,k_2,k_3)$ contains a subdivision of $B(k_1,k_2;k_3)$. As evidence, we prove this conjecture for $k_2=1$ (and $k_1, k_3$ arbitrary).<\/jats:p>","DOI":"10.37236\/6922","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:24:28Z","timestamp":1578651868000},"source":"Crossref","is-referenced-by-count":0,"title":["Bispindles in Strongly Connected Digraphs with Large Chromatic Number"],"prefix":"10.37236","volume":"25","author":[{"given":"Nathann","family":"Cohen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Havet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William","family":"Lochet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raul","family":"Lopes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,6,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:33:18Z","timestamp":1579217598000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,8]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6922","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,6,8]]},"article-number":"P2.39"}}