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Uniform { C h , S ( C h )}-Factorizations of K n − I for Even h

Author

Listed:
  • Giovanni Lo Faro

    (Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98100 Messina, Italy)

  • Salvatore Milici

    (Dipartimento di Matematica e Informatica, Università di Catania, 95124 Catania, Italy)

  • Antoinette Tripodi

    (Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98100 Messina, Italy)

Abstract

Let H be a connected subgraph of a graph G . An H -factor of G is a spanning subgraph of G whose components are isomorphic to H . Given a set H of mutually non-isomorphic graphs, a uniform H -factorization of G is a partition of the edges of G into H -factors for some H ∈ H . In this article, we give a complete solution to the existence problem of uniform H -factorizations of K n − I (the graph obtained by removing a 1-factor from the complete graph K n ) for H = { C h , S ( C h ) } , where C h is a cycle of length an even integer h ≥ 4 and S ( C h ) is the graph consisting of the cycle C h with a pendant edge attached to each vertex.

Suggested Citation

  • Giovanni Lo Faro & Salvatore Milici & Antoinette Tripodi, 2023. "Uniform { C h , S ( C h )}-Factorizations of K n − I for Even h," Mathematics, MDPI, vol. 11(16), pages 1-8, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3479-:d:1215500
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    References listed on IDEAS

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    1. Giovanni Lo Faro & Salvatore Milici & Antoinette Tripodi, 2020. "Uniformly Resolvable Decompositions of K v - I into n -Cycles and n -Stars, for Even n," Mathematics, MDPI, vol. 8(10), pages 1-9, October.
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