By Jiří Matousek, Jaroslav Nešetřil, Marco Pellegrini
ISBN-10: 8876425241
ISBN-13: 9788876425240
ISBN-10: 887642525X
ISBN-13: 9788876425257
This publication collects a few surveys on present developments in discrete arithmetic and discrete geometry. The components lined contain: graph representations, structural graphs thought, extremal graph idea, Ramsey concept and restricted pride problems.
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Example text
Z. RUZSA, On difference sets, Studia Sci. Math. Hungar. 13 (1978), 319–326. A coding problem for pairs of subsets Béla Bollobás, Zoltán Füredi, Ida Kantor, Gyula O. H. Katona and Imre Leader Abstract. Let X be an n–element finite set, 0 < k ≤ n/2 an integer. Suppose that {A1 , A2 } and {B1 , B2 } are pairs of disjoint k-element subsets of X (that is, |A1 | = |A2 | = |B1 | = |B2 | = k, A1 ∩ A2 = ∅, B1 ∩ B2 = ∅). Define the distance of these pairs by d({A1 , A2 }, {B1 , B2 }) = min{|A1 − B1 | + |A2 − B2 |, |A1 − B2 | + |A2 − B1 |}.
One of the results of [1] is a complete characterization of all heroes. 1. If H1 and H2 are heroes, then so is H1 ⇒ H2 . 2. Let H1 , H2 be non-null tournaments, and let H be H1 ⇒ H2 . Let m = max(|V (H1 )|, |V (H2 )|). Then every H -free tournament admits an ({H1 , H2 }, 2(m + 1)m )-partition. 1. 3. Let H1 , H2 be non-null tournaments, and let H be H1 ⇒ H2 . Assume that for i = 1, 2 every every Hi -free tournament has chromatic number at most di . Let m = max(|V (H1 )|, |V (H2 )|) and let d = max(d1 , d2 ).
Math. Soc. 24 (1981), 321–325. [31] H. T. V RE C´ ICA, On generalizations of Radon’s theorem and the Ham sandwich theorem, European J. Comb. 14 (1993), 259–264. [32] G. M. Z IEGLER, 3N Colored Points in a Plane, Notices of the AMS. 58 (2011), 550–557. [33] R. T. T. V RE C´ ICA, The colored Tverberg’s problem and complexes of injective functions, J. Comb. Theory A. 61 (1992), 309–318. [34] M. Y U . Z VAGELSKII, An elementary proof of Tverberg’s theorem, J. Math. Sci. ) 161 (2009), 384–387. Cliques and stable sets in undirected graphs Maria Chudnovsky Abstract.
Geometry, Structure and Randomness in Combinatorics by Jiří Matousek, Jaroslav Nešetřil, Marco Pellegrini
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