Temat: intersecting family - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Erdös-Ko-Rado from intersecting shadows
Autorzy:: Katona, Gyula
Kisvölcsey, Ákos
Powiązania:: https://bibliotekanauki.pl/articles/743244.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Kneser graph
coclique
intersecting family
shadow
Opis:: A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results.
Źródło:: Discussiones Mathematicae Graph Theory; 2012, 32, 2; 379-382
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A hierarchy of maximal intersecting triple systems
Autorzy:: Polcyn, J.
Ruciński, A.
Powiązania:: https://bibliotekanauki.pl/articles/254859.pdf
Data publikacji:: 2017
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: maximal intersecting family
3-uniform hypergraph
triple system
Opis:: We reach beyond the celebrated theorems of Erdös-Ko-Rado and Hilton-Milner, and a recent theorem of Han-Kohayakawa, and determine all maximal intersecting triples systems. It turns out that for each n ≥ 7 there are exactly 15 pairwise non-isomorphic such systems (and 13 for n = 6). We present our result in terms of a hierarchy of Turan numbers [formula], s ≥ 1, where [formula] is a pair of disjoint triples. Moreover, owing to our unified approach, we provide short proofs of the above mentioned results (for triple systems only). The triangle C3 is defined as C3 = {{x1,y3,x2}, {x1,y2,x3}, {x2, y1,x3}}. Along the way we show that the largest intersecting triple system H on n ≥ 6 vertices, which is not a star and is triangle-free, consists of max{10, n} triples. This facilitates our main proof's philosophy which is to assume that H contains a copy of the triangle and analyze how the remaining edges of H intersect that copy.
Źródło:: Opuscula Mathematica; 2017, 37, 4; 597-608
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: A general 2-part Erdös-Ko-Rado theorem
Autorzy:: Katona, G. O. H.
Powiązania:: https://bibliotekanauki.pl/articles/254727.pdf
Data publikacji:: 2017
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: extremal set theory
two-part problem
intersecting family
Opis:: A two-part extension of the famous Erdös-Ko-Rado Theorem is proved. The underlying set is partitioned into X1 and X2. Some positive integers [formula] are given. We prove that if F is an intersecting family containing members F such that [formula] holds for one of the values I (l ≤ i ≤ m) then |F| cannot exceed the size of the largest subfamily containing one element.
Źródło:: Opuscula Mathematica; 2017, 37, 4; 577-588
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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