which point sets admit a $k$-angulation?

أيُّ مجموعات النقاط تقبل $k$-تضليعاً؟

Clicks: 32
ID: 150264
2014
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Abstract
For \(k\ge 3\), a \(k\)-angulation is a 2-connected plane graph in which every internal face is a \(k\)-gon. We say that a point set \(P\) admits a plane graph \(G\) if there is a straight-line drawing of \(G\) that maps \(V(G)\) onto \(P\) and has the same facial cycles and outer face as \(G\). We investigate the conditions under which a point set \(P\) admits a \(k\)-angulation and find that, for sets containing at least \(2k^2\) points, the only obstructions are those that follow from Euler's formula.
لكل \(k\ge 3\)، يُعرَّف التقسيم إلى \(k\)-أضلاع (\(k\)-angulation) بأنه بيان مستوٍ ثنائي الترابط يكون فيه كل وجه داخلي مضلعاً ذا \(k\) أضلاع. ونقول إن مجموعة نقاط \(P\) تقبل بياناً مستوياً \(G\) إذا وُجد رسم بخطوط مستقيمة للبيان \(G\) ينقل \(V(G)\) على \(P\) ويمتلك دورات الوجوه والوجه الخارجي نفسها الخاصة بالبيان \(G\). ونستقصي الشروط التي تقبل بموجبها مجموعة نقاط \(P\) تقسيماً إلى \(k\)-أضلاع، ونجد أنه بالنسبة للمجموعات التي تحوي ما لا يقل عن \(2k^2\) نقطة، فإن العوائق الوحيدة هي تلك الناتجة عن صيغة أويلر.
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payne2014journalwhich Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Michael S. Payne, Jens M. Schmidt, David R. Wood
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Journal canadian journal of infectious diseases and medical microbiology
Year 2014
DOI
10.20382/jocg.v5i1a3
URL
http://jocg.org/index.php/jocg/article/view/92
Keywords Keywords not found

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