Highly Symmetric Subgraphs of Hypercubes
نویسندگان
چکیده
Two questions are considered, namely (i) How many colors are needed for a coloring of the n-cube without monochromatic quadrangles or hexagons? We show that four colors suffice and thereby settle a problem of Erdos. (ii) Which vertex-transitive induced subgraphs does a hypercube have? An interesting graph has come up in this context: If we delete a Hamming code from the 7-cube, the resulting graph is 6-regular, vertex-transitive and its edges can be two-colored such that the two monochromatic subgraphs are isomorphic, cubic, edge-transitive, nonvertex-transitive graphs of girth 10.
منابع مشابه
خواص متریک و ترکیبیاتی مکعبهای فیبوناتچی و لوکاس
An n-dimensional hypercube, Q_n, is a graph in which vertices are binary strings of length n where two vertices are adjacent if they differ in exactly one coordinate. Hypercubes and their subgraphs have a lot of applications in different fields of science, specially in computer science. This is the reason why they have been investigated by many authors during the years. Some of their subgraphs ...
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