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Computer-Based Design to Improve Bacillus thuringiensis Chitinase for Industrial Applications. [PDF]

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Complexes of Directed Graphs

SIAM Journal on Discrete Mathematics, 1999
A property \(P\) of graphs is called monotone if it is preserved under the deletion of edges. Let \(\Delta^P_n\) denote the simplicial complex whose simplices are edge sets of \(n\)-vertex graphs having a monotone property \(P\). Topological properties of complexes of undirected graphs recently have been studied in a number of papers (see references in
Anders Björner, Volkmar Welker
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Rankings of Directed Graphs

SIAM Journal on Discrete Mathematics, 1999
A ranking of a (di)graph is a colouring of the vertex set with positive integers in such a way that every (di)path between two vertices of the same colour has a vertex of larger colour. The \(k\)-ranking problem is as follows: given a (di)graph \(G\) and an integer \(k\), check whether \(G\) has a ranking with \(k\) colours. This problem is known to be
Jan Kratochvíl, Zsolt Tuza
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Directed hamiltonian graphs

Journal of Graph Theory, 1992
AbstractWe give a new condition involving degrees sufficient for a digraph to be hamiltonian.
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Independent Directed Triangles in a Directed Graph

Graphs and Combinatorics, 2000
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