{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:16Z","timestamp":1753893796700,"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>Let $G^{\\times}_{+}$ be the graph on the vertex-set the positive integers ${\\Bbb{N}}$, with $n$ joined to $m$ if $n\\neq m$ and for some $x,y\\in{\\Bbb{N}}$ we have $x+y=n$ and $x\\cdot y=m$. A pair of triangles sharing an edge (i.e., a $K_4$ with an edge deleted) and containing three consecutive numbers is called a $2$-fan, and three triangles on five numbers having one number in common and containing four consecutive numbers is called a $3$-fan. It will be shown that $G^{\\times}_{+}$ contains $3$-fans, infinitely many $2$-fans and even arbitrarily large \"bundles\" of triangles sharing an edge. Finally, it will be shown that $\\chi\\big(G^{\\times}_{+}\\big)\\ge 4$.<\/jats:p>","DOI":"10.37236\/1759","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:23:49Z","timestamp":1578720229000},"source":"Crossref","is-referenced-by-count":2,"title":["Fans and Bundles in the Graph of Pairwise Sums and Products"],"prefix":"10.37236","volume":"11","author":[{"given":"Lorenz","family":"Halbeisen","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,1,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:05:07Z","timestamp":1579323907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1759","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,1,2]]},"article-number":"R6"}}