Valery Gochev

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A path covering of a graph is a set of vertex-disjoint simple paths that cover all the vertices of the graph. We consider the graph Q n , the n-dimensional hypercube. The vertices of Q n are n-tuples of 0s and 1s; we say that a vertex is even if it has an even number of 1s and odd otherwise. In Q n , let F be a set of f 1 odd and f 2 even vertices, and let(More)
Let Qn be the n−dimensional binary hypercube, u 1 , u 2 and u 3 be distinct even vertices of Qn and v 1 , v 2 and v 3 be distinct odd vertices of Qn. We prove that if n ≥ 4, then there exist three paths in Qn, one joining u 1 and v 1 , one joining u 2 and u 3 and one joining v 2 and v 3 , such that every vertex of Qn belongs to exactly one of the paths.
In 2007, in their paper Path coverings with prescribed ends in faulty hypercubes, N. Castañeda and I. Gotchev formulated the following conjecture: Let n and k be positive integers with n ≥ k + 3 and F be a set of k even (odd) and k + 1 odd (even) vertices in the binary hypercube Qn. If u 1 and u 2 are two distinct even (odd) vertices in Qn − F then for Qn −(More)
Let n ≥ 5 and Q n be the n−dimensional binary hy-percube. Also, let u be a faulty even (odd) vertex in Q n , u 1 and u 2 be distinct even (odd) vertices of Q n − {u} and v 1 , v 2 , v 3 and v 4 be distinct odd (even) vertices of Q n − {u}. We prove that there exist three paths in Q n − {u}, one joining u 1 and u 2 , one joining v 1 and v 2 and one joining v(More)
We address questions of when (C(X), +) is a topological group in some topolo-gies which are meets of systems of compact-open topologies from certain dense subsets of X. These topologies have arisen from the theory of epimorphisms in lattice-ordered groups (in this context called " epi-topology "). A basic necessary and sufficient condition is developed,(More)
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