Temat: Folkman number - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A Note on Upper Bounds for Some Generalized Folkman Numbers
Autorzy:: Xu, Xiaodong
Liang, Meilian
Radziszowski, Stanisław
Powiązania:: https://bibliotekanauki.pl/articles/31343184.pdf
Data publikacji:: 2019-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Folkman number
Ramsey number
Opis:: We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special cases of generalized edge Folkman numbers, including the cases F_e(K₃, K₄ − e; K₅) ≤ 27 and F_e(K₄ − e, K₄ − e; K₅) ≤ 51. The latter bound follows from a construction of a K₅-free graph on 51 vertices, for which every edge coloring with two colors contains a monochromatic K₄ − e.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 4; 939-950
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Ramsey Properties of Random Graphs and Folkman Numbers
Autorzy:: Rödl, Vojtěch
Ruciński, Andrzej
Schacht, Mathias
Powiązania:: https://bibliotekanauki.pl/articles/31341650.pdf
Data publikacji:: 2017-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Ramsey property
random graph
Folkman number
Opis:: For two graphs, G and F, and an integer r ≥ 2 we write G → (F)_r if every r-coloring of the edges of G results in a monochromatic copy of F. In 1995, the first two authors established a threshold edge probability for the Ramsey property G(n, p) → (F)_r, where G(n, p) is a random graph obtained by including each edge of the complete graph on n vertices, independently, with probability p. The original proof was based on the regularity lemma of Szemerédi and this led to tower-type dependencies between the involved parameters. Here, for r = 2, we provide a self-contained proof of a quantitative version of the Ramsey threshold theorem with only double exponential dependencies between the constants. As a corollary we obtain a double exponential upper bound on the 2-color Folkman numbers. By a different proof technique, a similar result was obtained independently by Conlon and Gowers.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 3; 755-776
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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