Proof of the (n/2-n/2-n/2) Conjecture for Large n
نویسنده
چکیده
A conjecture of Loebl, also known as the (n/2 − n/2 − n/2) Conjecture, states that if G is an n-vertex graph in which at least n/2 of the vertices have degree at least n/2, then G contains all trees with at most n/2 edges as subgraphs. Applying the Regularity Lemma, Ajtai, Komlós and Szemerédi proved an approximate version of this conjecture. We prove it exactly for sufficiently large n. This immediately gives a tight upper bound for the Ramsey number of trees, and partially confirms a conjecture of Burr and Erdős.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 18 شماره
صفحات -
تاریخ انتشار 2011