Uniform {Ch,S(Ch)}-Factorizations of Kn−I for Even h

Lo Faro, Giovanni; Milici, Salvatore; Tripodi, Antoinette

doi:10.3390/math11163479

Open AccessArticle

Uniform {C_h,S(C_h)}-Factorizations of K_n−I for Even h

by

Giovanni Lo Faro

¹

,

Salvatore Milici

^2,*

and

Antoinette Tripodi

¹

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

²

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

^*

Author to whom correspondence should be addressed.

Mathematics 2023, 11(16), 3479; https://doi.org/10.3390/math11163479

Submission received: 3 July 2023 / Revised: 3 August 2023 / Accepted: 7 August 2023 / Published: 11 August 2023

(This article belongs to the Special Issue Advances in Design Theory, Combinatorial Algebraic Geometry and Applications)

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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 \in 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 \geq 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

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MDPI and ACS Style

Lo Faro, G.; Milici, S.; Tripodi, A. Uniform {C_h,S(C_h)}-Factorizations of K_n−I for Even h. Mathematics 2023, 11, 3479. https://doi.org/10.3390/math11163479

AMA Style

Lo Faro G, Milici S, Tripodi A. Uniform {C_h,S(C_h)}-Factorizations of K_n−I for Even h. Mathematics. 2023; 11(16):3479. https://doi.org/10.3390/math11163479

Chicago/Turabian Style

Lo Faro, Giovanni, Salvatore Milici, and Antoinette Tripodi. 2023. "Uniform {C_h,S(C_h)}-Factorizations of K_n−I for Even h" Mathematics 11, no. 16: 3479. https://doi.org/10.3390/math11163479

APA Style

Lo Faro, G., Milici, S., & Tripodi, A. (2023). Uniform {C_h,S(C_h)}-Factorizations of K_n−I for Even h. Mathematics, 11(16), 3479. https://doi.org/10.3390/math11163479

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Uniform {C_h,S(C_h)}-Factorizations of K_n−I for Even h

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