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

Giovanni Lo Faro, Salvatore Milici () and Antoinette Tripodi
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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

Mathematics, 2023, vol. 11, issue 16, 1-8

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.

Keywords: graph decompostion; factor; uniform factorization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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