منابع مشابه
Kernels in edge coloured line digraph
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satisfies the two following conditions (i) for every pair of different vertices u, v ∈ N there is no monochromatic directed path between t...
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Known facts: the decision problem of the existence of a kernel in a digraph G = (V; E) is NP-complete; if all of the cycles of G have even length, then G has a kernel; and the question of the number of kernels is #P-complete even for this restricted class of digraphs. We construct game theory tools, of independent interest, concerning strategies in the presence of draw positions, to show, in th...
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Given a digraph D = (V, A), a quasi-kernel of D is an independent set Q C_ V such that for every vertex v not contained in Q, either there exists a vertex u E Q such that v dominates u, or there exists a vertex w such that v dominates w and w dominates some vertex u E Q. A sink in a digraph D = (V, A) is a vertex v E V that dominates no vertex of D. In this thesis we prove that if D is a semico...
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In 1964 Černý conjectured that each n-state synchronizing automaton posesses a reset word of length at most (n − 1). From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in n. Thus the main problem here is to prove quadratic (in n) upper bounds. Since 1964, this problem has been solved for few special classes of synchronizing automata. One ...
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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0035-3