A note on self-complementary 4-uniform hypergraphs

• Autorzy: Szymański A.
• Języki publikacji: EN

Abstrakty

EN

We prove that a permutation theta is complementing permutation for a 4-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of theta is a multiple of 8, (ii) theta has 1, 2 or 3 fixed points, and all other cycles have length a multiple of 8, (iii) theta has 1 cycle of length 2, and all other cycles have length a multiple of 8, (iv) theta has 1 fixed point, 1 cycle of length 2, and all other cycles have length a multiple of 8, (v) theta has 1 cycle of length 3, and all other cycles have length a multiple of 8. Moreover, we present algorithms for generating every possible 3 and 4-uniform self-complementary hypergraph.

Słowa kluczowe

EN

complementing permutation; self-complementary hypergraph; k-uniform hypergraph

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 2
• Strony: 319--323
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Szymański A.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland,

Bibliografia

• [1] Kocay W.: Reconstructing Graphs as Subsumed Graphs of Hypergraphs, and Some Self-Complementary Triple Systems. Graphs and Combinatorics 8 (1992) 259-276.
• [2] Ringel G.: Selbstkomplemenfdre Graphen. Arch. Math. 14 (1963) 354-358.
• [3] Sachs H.: Uber selbstkomplementare graphen. Publ. Math. Debrecen 9 (1962) 270-288.