Maximum degree and fractional matchings in uniform hypergraphs

@article{Fredi1981MaximumDA,
  title={Maximum degree and fractional matchings in uniform hypergraphs},
  author={Z. F{\"u}redi},
  journal={Combinatorica},
  year={1981},
  volume={1},
  pages={155-162}
}
  • Z. Füredi
  • Published 1981
  • Mathematics, Computer Science
  • Combinatorica
AbstractLet ℋ be a family ofr-subsets of a finite setX. SetD(ℋ)= $$\mathop {\max }\limits_{x \in X} $$ |{E:x∈E∈ℋ}|, (maximum degree). We say that ℋ is intersecting if for anyH,H′ ∈ ℋ we haveH ∩H′ ≠ 0. In this case, obviously,D(ℋ)≧|ℋ|/r. According to a well-known conjectureD(ℋ)≧|ℋ|/(r−1+1/r). We prove a slightly stronger result. Let ℋ be anr-uniform, intersecting hypergraph. Then either it is a projective plane of orderr−1, consequentlyD(ℋ)=|ℋ|/(r−1+1/r), orD(ℋ)≧|ℋ|/(r−1). This is a corollary to… Expand
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