منابع مشابه
Unavoidable 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 ...
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We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgraph of the de Bruijn graph and which we prove to be Hamiltonian. In other cases we reduce a problem under con...
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A word w is said to contain the pattern P if there is a way to substitute a nonempty word for each letter in P so that the resulting word is a subword of w. Bean, Ehrenfeucht and McNulty and, independently, Zimin characterised the patterns P which are unavoidable, in the sense that any sufficiently long word over a fixed alphabet contains P . Zimin’s characterisation says that a pattern is unav...
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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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2008
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2008.04.003