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An n-bit (cyclic) Gray code is a (cyclic) sequence of all n-bit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an n-bit cyclic Gray code whose graph of transitions is the d-dimensional hypercube Qd if n = 2d, or a subgraph of Qd...
We study a (k + 1)-coloring problem in a class of (k,s)-dart graphs, k,s ≥ 2, where each vertex of degree at least k + 2 belongs to a (k,i)-diamond, i ≤ s. We prove that dichotomy holds, that means the problem is either NP-complete (if k < s), or can be solved in linear time (if k ≥ s). In particular, in the latter case we generalize the classical Brooks Theorem, that means we prove that a (k,...
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