Geodesic
A note on acyclic number of planar graphs
Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 317-322.

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The acyclic number a(G) of a graph G is the maximum order of an induced forest in G. The purpose of this short paper is to propose a conjecture that a(G) ≥ (1 − 3/(2g))n holds for every planar graph G of girth g and order n, which captures three known conjectures on the topic. In support of this conjecture, we prove a weaker result that a(G) ≥ (1 − 3/g)n holds. In addition, we give a construction showing that the constant 3/2 from the conjecture cannot be decreased.
DOI : 10.26493/1855-3974.1118.143
Keywords: Induced forest, acyclic number, planar graph, girth 
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Mirko Petruševski; Riste Škrekovski. A note on acyclic number of planar graphs. Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 317-322. doi : 10.26493/1855-3974.1118.143. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1118.143/

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