The Loebl-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Details The Loebl-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars The Loebl-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

2007-12-20

arxiv.org/abs/0712.3382v1

Mathematics

Combinatorics

11 pages, 1 figure

Scientific paper

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a
graph G have degree at least some k, 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,F) of trees T, F from the above classes.

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