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arXiv · 1705.11133

A lower bound on the order of the largest induced linear forest in triangle-free planar graphs

François Dross·Mickael Montassier·Alexandre Pinlou
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Abstract

We prove that every triangle-free planar graph of order $n$ and size $m$ has an induced linear forest with at least $\frac{9n - 2m}{11}$ vertices, and thus at least $\frac{5n + 8}{11}$ vertices. Furthermore, we show that there are triangle-free planar graphs on $n$ vertices whose largest induced linear forest has order $\lceil \frac{n}{2} \rceil + 1$.

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François Dross, Mickael Montassier, Alexandre Pinlou. 2017-05-31. A lower bound on the order of the largest induced linear forest in triangle-free planar graphs. https://arxiv.org/abs/1705.11133

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