A note on k-uniform self-complementary hypergraphs of given order
نویسندگان
چکیده
We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if ( n k ) is even.
منابع مشابه
Self-Complementary Hypergraphs
In this thesis, we survey the current research into self-complementary hypergraphs, and present several new results. We characterize the cycle type of the permutations on n elements with order equal to a power of 2 which are k-complementing. The k-complementing permutations map the edges of a k-uniform hypergraph to the edges of its complement. This yields a test to determine whether a finite p...
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In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive selfcomplementary k-uniform hypergraph of order n, where k = 2 or k = 2 + 1 and n ≡ 1 (mod 2), then the highest power of any prime dividing n must be congruent to 1 modulo 2. We show that this necessary condition is also sufficient in ...
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For a positive integer q, a k-uniform hypergraph X = (V,E) is q-complementary if there exists a permutation θ on V such that the sets E,E, E 2 , . . . , E q−1 partition the set of k-subsets of V . The permutation θ is called a q-antimorphism of X. The well studied self-complementary uniform hypergraphs are 2-complementary. For an integer n and a prime p, let n(p) = max{i : p i divides n}. In th...
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A k-uniform hypergraphH = (V ;E) is said to be self-complementary whenever it is isomorphic with its complement H = (V ; ` V k ́ −E). Every permutation σ of the set V such that σ(e) is an edge ofH if and only if e ∈ E is called selfcomplementing. 2-self-comlementary hypergraphs are exactly self complementary graphs introduced independently by Ringel (1963) and Sachs (1962). For any positive inte...
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 29 شماره
صفحات -
تاریخ انتشار 2009