Abstract
Let t(G) denote cardinality of a maximum induced forest of a graph G with n vertices. For connected simple cubic graphs G without triangles, it is shown that t(G)⩾2n3 except for two particular graphs. This lower bound is sharp and it improves a result due to J.A. Bondy, et al. [1]. Using this result, we show that Ewald Speckenmeyer's Conjecture, i.e. t(G)⩾2n3 for all biconnected cubic graphs G with girth 4, is true, except for two particular graphs, which we describe.
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