منابع مشابه
Toroidal Grids Are Anti-magic
An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the integers {1, ..., q} such that all p vertex sums are pairwise distinct, where the vertex sum on a vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it has an anti-magic labeling. Hartsfield and Ringel [3] conjectured t...
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The problem on the Hamiltonicity of graphs is well studied in discrete algorithm and graph theory, because of its relation to traveling salesman problem (TSP). Starting with Tutte’s result, stating that every 4-connected planar graph is Hamiltonian, several researchers have studied the Hamiltonicity of graphs on surfaces. Extending Tutte’s technique, Thomassen proved that every 4-connected plan...
متن کاملFive-Connected Toroidal Graphs Are Hamiltonian
It is well known that not all 3-connected planar graphs are hamiltonian. Whitney [10] proved that every triangulation of the sphere with no separating triangles is hamiltonian. Tutte [9] proved that every 4-connected planar graph has a Hamilton cycle. Extending Tutte's technique, Thomassen [8] proved that every 4-connected planar graph is in fact Hamilton connected. (A small omission in [8] was...
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We present quantitative models for the selection pressure of cellular evolutionary algorithms structured in two dimensional regular lattices. We derive models based on probabilistic difference equations for synchronous and several asynchronous cell update policies. Theoretical results are in agreement with experimental values and show that the selection intensity can be controlled by using diff...
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We have developed a unique multicellular aggregate formation platform that utilizes a maskless gray-scale photolithography. The cellular aggregate formed using this platform has a toroidal-like geometry and includes a micro-pore that facilitates the supply of the oxygen and growth factors and expels waste products. As a result, this platform was capable of rapidly producing hundreds of multicel...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2037657