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تسجيل مستخدم جديدكوبونات جزئية: الهياكل والتشخيصات والبناء
Partial cubes: structures, characterizations, and constructions
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تأليف
Sergei Ovchinnikov
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تتألف المكعبات الجزئية من شبكات إيزومترية من المكعبات المتعددة الأبعاد. تلعب الهياكل المحددة على الشبكة بواسطة المكعبات النصفية والعلاقات ديوكوفيتش ووينكلر دوراً مهماً في نظرية المكعبات الجزئية. يستخدم هذه الهياكل في الورقة لتشخيص الشبكات الثنائية والمكعبات الجزئية لأي بعد. وتم إنشاء تشخيصات جديدة وإعطاء دلائل جديدة لبعض النتائج المعروفة. يستخدم العمليات المنتج الكارتزي واللصق والتوسع والضغط في الورقة لإنشاء مكعبات جزئية جديدة من القديمة. وبالأخص، يتم حساب الأبعاد الإيزومترية والشبكية للمكعبات الجزئية المحدودة التي تم الحصول عليها بواسطة هذه العمليات.
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi{c}s and Winklers relations play an important role in the theory of partial cubes. These structures are employed in the paper to characterize bipartite graphs and partial cubes of arbitrary dimension. New characterizations are established and new proofs of some known results are given. The operations of Cartesian product and pasting, and expansion and contraction processes are utilized in the paper to construct new partial cubes from old ones. In particular, the isometric and lattice dimensions of finite partial cubes obtained by means of these operations are calculated.
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