# A greedy algorithm for finding a large 2-matching on a random cubic graph

Deepak Bal, Patrick Bennett, Tom Bohman, Alan Frieze

Research output: Contribution to journalArticle

### 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 κ denotes the number of components. In this article, we analyze the performance of a greedy algorithm 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)=Θ(n1/5).

Original language English 449-481 33 Journal of Graph Theory 88 3 https://doi.org/10.1002/jgt.22224 Published - Jul 2018

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Cubic Graph
Greedy Algorithm
Random Graphs
Spanning Subgraph
Number of Components
Regular Graph
Maximum Degree
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### Keywords

• 2-matching
• greedy algorithm
• random cubic graph

### Cite this

Bal, Deepak ; Bennett, Patrick ; Bohman, Tom ; Frieze, Alan. / A greedy algorithm for finding a large 2-matching on a random cubic graph. In: Journal of Graph Theory. 2018 ; Vol. 88, No. 3. pp. 449-481.
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A greedy algorithm for finding a large 2-matching on a random cubic graph. / Bal, Deepak; Bennett, Patrick; Bohman, Tom; Frieze, Alan.

In: Journal of Graph Theory, Vol. 88, No. 3, 07.2018, p. 449-481.

Research output: Contribution to journalArticle

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