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- W4300428652 abstract "Given an edge-colored complete graph $K_n$ on $n$ vertices, a perfect (respectively, near-perfect) matching $M$ in $K_n$ with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors. In this paper, we consider an edge coloring of $K_n$ by circular distance, and we denote the resulting complete graph by $K^{bullet}_n$. We show that when $K^{bullet}_n$ has an even number of vertices, it contains a rainbow perfect matching if and only if $n=8k$ or $n=8k+2$, where $k$ is a nonnegative integer. In the case of an odd number of vertices, Kirkman matching is known to be a rainbow near-perfect matching in $K^{bullet}_n$. However, real-world applications sometimes require multiple rainbow near-perfect matchings. We propose a method for using a recursive algorithm to generate multiple rainbow near-perfect matchings in $K^{bullet}_n$." @default.
- W4300428652 created "2022-10-03" @default.
- W4300428652 creator A5041823290 @default.
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- W4300428652 date "2020-12-10" @default.
- W4300428652 modified "2023-09-26" @default.
- W4300428652 title "Rainbow Perfect and Near-Perfect Matchings in Complete Graphs with Edges Colored by Circular Distance" @default.
- W4300428652 doi "https://doi.org/10.48550/arxiv.2012.06083" @default.
- W4300428652 hasPublicationYear "2020" @default.
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