A greedy algorithm for finding a large 2-matching on a random cubic graph
Abstract
A 2-matching of a graph $G$ is a spanning subgraph with maximum degree two. The size of a 2-matching $U$ is the number of edges in $U$ and this is at least $n-\k(U)$ where $n$ is the number of vertices of $G$ and $\k$ denotes the number of components. In this paper, we analyze the performance of a greedy algorithm \textsc{2greedy} for finding a large 2-matching on a random 3-regular graph. We prove that with high probability, the algorithm outputs a 2-matching $U$ with $\k(U) = \tilde{\Theta}\of{n^{1/5}}$.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2012
- DOI:
- 10.48550/arXiv.1209.6570
- arXiv:
- arXiv:1209.6570
- Bibcode:
- 2012arXiv1209.6570B
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics
- E-Print:
- 23pp