The decycling numbers of graphs

Details The decycling numbers of graphs The decycling numbers of graphs

2007-03-19

arxiv.org/abs/math/0703544v1

Australasian Journal of Combinatorics 25(2002), 285-298

Mathematics

Combinatorics

Scientific paper

For a graph $G$ and $S\subset V(G)$, if $G - S$ is acyclic, then $S$ is said to be a decycling set of $G$. The size of a smallest decycling set of $G$ is called the decycling number of $G$. The purpose of this paper is a comprehensive review of recent results and several open problems on this graph parameter. Results to be reviewed include recent work on decycling numbers of cubes, grids and snakes. A structural description of graphs with a fixed decycling number based on connectivity is also presented. Graphs with small decycling numbers are characterized.

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