Geodesic
Induced trees in triangle-free graphs
The electronic journal of combinatorics, Tome 15 (2008)
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We prove that every connected triangle-free graph on $n$ vertices contains an induced tree on $\exp(c\sqrt{\log n}\,)$ vertices, where $c$ is a positive constant. The best known upper bound is $(2+o(1))\sqrt n$. This partially answers questions of Erdős, Saks, and Sós and of Pultr.
DOI : 10.37236/765
Classification : 05C55, 05C05
Mots-clés : connected triangle free graph, number of vertices of an induced tree, upper bound, blow-up construction 
@article{10_37236_765,
     author = {Ji\v{r}{\'\i} Matou\v{s}ek and Robert \v{S}\'amal},
     title = {Induced trees in triangle-free graphs},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/765},
     zbl = {1159.05035},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/765/}
}
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Jiří Matoušek; Robert Šámal. Induced trees in triangle-free graphs. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/765

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