The existence of bipartite almost self-complementary 3-uniform hypergraphs

• Autorzy: Kamble L. N. , Deshpande C. M. , Athawale B. P.

Identyfikatory

DOI

10.7494/OpMath.2023.43.5.663

• Języki publikacji: EN

Abstrakty

EN

An almost self-complementary 3-uniform hypergraph on n vertices exists if and only if n is congruent to 3 modulo 4. A hypergraph H with vertex set V and edge set E is called bipartite if V can be partitioned into two subsets V1 and V2 such that e ∩ V1 ̸= ∅ and e ∩ V2̸= ∅ for any e ∈ E. A bipartite self-complementary 3-uniform hypergraph H with partition (V1, V2) of the vertex set V such that |V1| = m and |V2| = n exists if and only if either (i) m = n or (ii) m ̸= n and either m or n is congruent to 0 modulo 4 or (iii) m ̸= n and both m and n are congruent to 1 or 2 modulo 4. In this paper we define a bipartite almost self-complementary 3-uniform hypergraph H with partition (V1, V2) of a vertex set V such that |V1| = m and |V2| = n and find the conditions on m and n for a bipartite 3-uniform hypergraph H to be almost self-complementary. We also prove the existence of bi-regular bipartite almost self-complementary 3-uniform hypergraphs.

Słowa kluczowe

EN

almost self-complementary 3-uniform hypergraph; bipartite hypergraph; bipartite self-complementary 3-uniform hypergraph; bipartite almost self-complementary 3-uniform hypergraph

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 5
• Strony: 663--673
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kamble L. N.

• MES’s Abasaheb Garware College, Pune, Department of Mathematics, Pune - 411004, Maharashtra, India

autor

Deshpande C. M.

• College of Engineering Pune, Department of Mathematics, Pune - 411005, Maharashtra, India

autor

Athawale B. P.

• College of Engineering Pune, Department of Mathematics, Pune - 411005, Maharashtra, India

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)