منابع مشابه
Unavoidable subtrees
Let Tk be a family of all k-vertex trees. For T ⊆ Tk and a tree T , we write T → T if T contains at least one of the trees from T as a subtree, we write T 6→ T otherwise. Let ex(T ) be the smallest integer n, if such exists, such that for any tree T on at least n vertices T → T . It is shown that min{ex(T ) : T ⊆ Tk, |T | = q} = 2 log q−1 , where logq−1 is the q− 1 times iterated logarithm. In ...
متن کاملUnavoidable and Almost Unavoidable Sets of Words
A set of words over a finite alphabet is called an unavoidable set if every word of sufficiently long length must contain some word from this set as a subword. Motivated by a theorem from automata theory, we introduce the notion of an almost unavoidable set and prove certain asymptotic estimates for the size of almost unavoidable sets of uniform length.
متن کاملSubtrees 1
The concepts of root tree, the set of successors of a node in decorated tree and sets of subtrees are introduced. Let us mention that every tree which is finite is also finite-order. Next we state three propositions: (1) For every decorated tree t holds tε N = t. (2) For every tree t and for all finite sequences p, q of elements of N such that p q ∈ t holds t(p q) = tpq. (3) Let t be a decorate...
متن کاملUnavoidable patterns
Let Fk denote the family of 2-edge-colored complete graphs on 2k vertices in which one color forms either a clique of order k or two disjoint cliques of order k. Bollobás conjectured that for every 2 > 0 and positive integer k there is an n(k, 2) such that every 2-edge-coloring of the complete graph of order n ≥ n(k, 2) which has at least 2n2 ) edges in each color contains a member of Fk. This ...
متن کاملUnavoidable arrays
An n × n array is avoidable if for each set of n symbols there is a Latin square on these symbols which differs from the array in every cell. We characterise all unavoidable square arrays with at most 2 symbols, and all unavoidable arrays of order at most 4. We also identify a number of general families of unavoidable arrays, which we conjecture to be a complete account of unavoidable arrays. N...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.01.015