MATHEMATICA BOHEMICA, Vol. 120, No. 3, pp. 305-317, 1995

Hamiltonian connectedness and a matching in powers of connected graphs

Elena Wisztova

Vysoka skola dopravy a spojov, Hurbanova 15, 010 26 Zilina, Slovakia

Abstract: In this paper the following results are proved: 1. Let $P_n$ be a path with $n$ vertices, where $n \geq5$ and $n \not= 7,8$. Let $M$ be a matching in $P_n$. Then $(P_n)^4 - M$ is hamiltonian-connected. 2. Let $G$ be a connected graph of order $p \geq5$, and let $M$ be a matching in $G$. Then $G^5 - M$ is hamiltonian-connected.

Keywords: power of a graph, matching, hamiltonian connectedness

Classification (MSC 1991): 05C70, 05C45


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