The Perfect Matching Hamiltonian property in Prism and Crossed Prism graphs

Fuente: arXiv
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Hauptverfasser: Colangelo, Francesco, Romaniello, Federico
Format: Preprint
Veröffentlicht: 2024
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author Colangelo, Francesco
Romaniello, Federico
author_facet Colangelo, Francesco
Romaniello, Federico
contents A graph $G$ has the \emph{Perfect Matching Hamiltonian property} (or for short, $G$ is $PMH$) if, for each one of its perfect matchings, there is another perfect matching of $G$ such that the union of the two perfect matchings yields a Hamiltonian cycle of $G$. In this note, we show that \emph{Prism graphs} $\cP_n$ are not $PMH$, except for the $Cube\ graph$, and indicate for which values of $n$ the \emph{Crossed Prism graphs} $\cCP_n$ are $PMH$.
format Preprint
id arxiv_https___arxiv_org_abs_2411_09724
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Perfect Matching Hamiltonian property in Prism and Crossed Prism graphs
Colangelo, Francesco
Romaniello, Federico
Combinatorics
05C15, 05C45, 05C70
A graph $G$ has the \emph{Perfect Matching Hamiltonian property} (or for short, $G$ is $PMH$) if, for each one of its perfect matchings, there is another perfect matching of $G$ such that the union of the two perfect matchings yields a Hamiltonian cycle of $G$. In this note, we show that \emph{Prism graphs} $\cP_n$ are not $PMH$, except for the $Cube\ graph$, and indicate for which values of $n$ the \emph{Crossed Prism graphs} $\cCP_n$ are $PMH$.
title The Perfect Matching Hamiltonian property in Prism and Crossed Prism graphs
topic Combinatorics
05C15, 05C45, 05C70
url https://arxiv.org/abs/2411.09724