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Displaying similar documents to “The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs”

Almost Self-Complementary 3-Uniform Hypergraphs

Lata N. Kamble, Charusheela M. Deshpande, Bhagyashree Y. Bam (2017)

Discussiones Mathematicae Graph Theory

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It is known that self-complementary 3-uniform hypergraphs on n vertices exist if and only if n is congruent to 0, 1 or 2 modulo 4. In this paper we define an almost self-complementary 3-uniform hypergraph on n vertices and prove that it exists if and only if n is congruent to 3 modulo 4. The structure of corresponding complementing permutation is also analyzed. Further, we prove that there does not exist a regular almost self-complementary 3-uniform hypergraph on n vertices where n is...

Maximum Hypergraphs without Regular Subgraphs

Jaehoon Kim, Alexandr V. Kostochka (2014)

Discussiones Mathematicae Graph Theory

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We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.

Trivial Jensen measures without regularity

J. F. Feinstein (2001)

Studia Mathematica

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In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.

Constrained Colouring and σ-Hypergraphs

Yair Caro, Josef Lauri, Christina Zarb (2015)

Discussiones Mathematicae Graph Theory

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A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours. This notion, introduced by Bujtás and Tuza, generalises both classical hypergraph colourings and more general Voloshin colourings of hypergraphs. In fact, for r-uniform hypergraphs, classical colourings correspond to (2, r)-colourings while an important instance of...

Self-complementary hypergraphs

A. Paweł Wojda (2006)

Discussiones Mathematicae Graph Theory

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A k-uniform hypergraph H = (V;E) is called self-complementary if there is a permutation σ:V → V, called self-complementing, such that for every k-subset e of V, e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with H ' = ( V ; V k - E ) . In the present paper, for every k, (1 ≤ k ≤ n), we give a characterization of self-complementig permutations of k-uniform self-complementary hypergraphs of the order n. This characterization implies the well known results for self-complementing permutations...