G-Intersecting Families

G-Intersecting Families

Let G be a graph on vertex set [n], and for X ⊆ [n] let N(X) be the union of X and its neighbourhood in G. A family of sets [Fscr ] ⊆ 2[n] is G-intersecting if N(X) ∩ Y ≠ [empty ] for all X, Y ∈ [Fscr ]. In this paper we study the cardinality and structure of the largest k-uniform G-intersecting fam...

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Veröffentlicht in:Combinatorics, probability & computing probability & computing, 2001-09, Vol.10 (5), p.367-384
Hauptverfasser: BOHMAN, TOM, FRIEZE, ALAN, RUSZINKÓ, MIKLÓS, THOMA, LUBOš
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Computation
Graphs
Scripts
Unions
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Zusammenfassung:Let G be a graph on vertex set [n], and for X ⊆ [n] let N(X) be the union of X and its neighbourhood in G. A family of sets [Fscr ] ⊆ 2[n] is G-intersecting if N(X) ∩ Y ≠ [empty ] for all X, Y ∈ [Fscr ]. In this paper we study the cardinality and structure of the largest k-uniform G-intersecting families on a fixed graph G.
ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548301004795