# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

J.J. Lin, M.J. Jou

Title:

Minimum coverings of crowns with cycles and stars

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-10-22, Revised: 2019-07-07, Accepted: 2019-07-07, https://doi.org/10.7151/dmgt.2241

Abstract:

Let $F$, $G$ and $H$ be graphs. A $(G,H)$-decomposition of $F$ is a partition of the edge set of $F$ into copies of $G$ and copies of $H$ with at least one copy of $G$ and at least one copy of $H$. For $R\subseteq F$, a $(G,H)$-covering of $F$ with padding $R$ is a $(G,H)$-decomposition of $F+E(R)$. A $(G,H)$-covering of $F$ with the smallest cardinality is a minimum $(G,H)$-covering. This paper gives the solution of finding the minimum $(C_k,S_k)$-covering of the crown $C_{n,n-1}$.

Keywords:

cycle, star, covering, decomposition, crown