Geodesic
The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars
The electronic journal of combinatorics, Tome 15 (2008)
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Loebl, Komlós, and Sós conjectured that if at least half the vertices of a graph $G$ have degree at least some $k\in \Bbb N$, then every tree with at most $k$ edges is a subgraph of $G$. We prove the conjecture for all trees of diameter at most $5$ and for a class of caterpillars. Our result implies a bound on the Ramsey number $r(T,T')$ of trees $T,T'$ from the above classes.
DOI : 10.37236/830
Classification : 05C05, 05C35 
@article{10_37236_830,
     author = {Diana Piguet and Maya Jakobine Stein},
     title = {The {Loebl-Koml\'os-S\'os} conjecture for trees of diameter 5 and for certain caterpillars},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/830},
     zbl = {1158.05315},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/830/}
}
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Diana Piguet; Maya Jakobine Stein. The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/830

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