{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T08:44:55Z","timestamp":1773477895988,"version":"3.50.1"},"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>We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph $G=(V,E)$ has a partition into two spanning trees $T_1$ and $T_2$ then there is a map $p:V\\to \\mathbb{R}^2$, $p(v)=(p_1(v),p_2(v))$, such that $|p_i(u)-p_i(v)| \\geqslant |p_{3-i}(u)-p_{3-i}(v)|$ for every edge $uv$ in $T_i$ ($i=1,2$). As a consequence, we solve an open problem on the realisability of minimally rigid bar-joint frameworks in the $\\ell^1$ or $\\ell^\\infty$-plane. We also show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.<\/jats:p>","DOI":"10.37236\/8196","type":"journal-article","created":{"date-parts":[[2020,6,26]],"date-time":"2020-06-26T00:52:24Z","timestamp":1593132744000},"source":"Crossref","is-referenced-by-count":1,"title":["Constructing Isostatic Frameworks for the $\\ell^1$ and $\\ell^\\infty$ Plane"],"prefix":"10.37236","volume":"27","author":[{"given":"Katie","family":"Clinch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Derek","family":"Kitson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,6,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p49\/8106","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p49\/8106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,26]],"date-time":"2020-06-26T00:52:39Z","timestamp":1593132759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,12]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/8196","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,12]]},"article-number":"P2.49"}}