Edge intersection graphs of linear 3-uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Edge intersection graphs of linear 3-uniform hypergraphs
Let L3 be the class of edge intersection graphs of linear 3-uniform hypergraphs. The problem of recognizing G ∈ L3 is NP-complete. Denote by δALG the minimal integer such that the problem ”G ∈ L3 ” is polynomially solvable in the class of graphs G with the minimal vertex degree δ(G) ≥ δALG and by δFIS the minimal integer such that L3 can be characterized by a finite list of forbidden induced su...
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The intersection graph or the line graph Ω(H) of a hypergraph H is defined as follows: 1) the vertices of Ω(H) are in a bijective correspondence with the edges of H, 2) two vertices are adjacent in Ω(H) if and only if the corresponding edges intersect. Characterizing and recognizing intersection graphs of hypergraphs with some additional property P is one of the central problems in intersection...
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Bollobás and Thomason conjectured that the vertices of any r-uniform hypergraph with m edges can be partitioned into r sets so that each set meets at least rm/(2r − 1) edges. For r = 3, Bollobás, Reed and Thomason proved the lower bound (1− 1/e)m/3 ≈ 0.21m, which was improved to 5m/9 by Bollobás and Scott (while the conjectured bound is 3m/5). In this paper, we show that this Bollobás-Thomason ...
متن کامل3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
Chvátal, Rödl, Szemerédi and Trotter [1] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform ‘pseudo-random’ hypergraphs. keywords: hypergraphs; regularity lemm...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.12.082