Hamiltonian-connected tournaments
نویسندگان
چکیده
منابع مشابه
Weakly Hamiltonian-connected ordinary multipartite tournaments
We characterize weakly Hamiltonian-connected ordinary multipartite tournaments. Our result generalizes such a characterization for tournaments by Thomassen and implies a polynomial algorithm to decide the existence of a Hamiltonian path connecting two given vertices in an ordinary multipartite tournament and find one, if it exists.
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Let T be a tournament and let D be a digraph. We say that T contains D if D is a subgraph of T. The order of a digraph D, denoted by |D|, is its number of vertices. Let x and y be two vertices of T. We write x y if (x, y) is an arc of T. Likewise, let X and Y be two subdigraphs of T. We write X Y if x y for all pairs (x, y) # V(X )_V(Y ). Let A1 , A2 , ..., Ak be a family of subdigraphs of T. W...
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Let Gn be the complete graph on the vertex set [n] = {1, 2, . . . , n} and ω an orientation of Gn , i.e., ω is an assignment of a direction i → j of each edge {i, j} of Gn . Let eq denote the qth unit coordinate vector of Rn . Write P(Gn ;ω) ⊂ R n for the convex hull of the (n 2 ) points ei − e j , where i → j is the direction of the edge {i, j} in the orientation ω. It will be proved that, for...
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We show that every regular tournament on n vertices has at least n!/(2+o(1)) Hamiltonian cycles, thus answering a question of Thomassen [17] and providing a partial answer to a question of Friedgut and Kahn [7]. This compares to an upper bound of about O(nn!/2) for arbitrary tournaments due to Friedgut and Kahn (somewhat improving Alon’s bound of O(nn!/2)). A key ingredient of the proof is a ma...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1980
ISSN: 0095-8956
DOI: 10.1016/0095-8956(80)90061-1