Hypergraphs with high projective dimension and 1-dimensional hypergraphs
نویسندگان
چکیده
منابع مشابه
Hypergraphs with high projective dimension and 1-dimensional hypergraphs
(Dual) hypergraphs have been used by Kimura, Rinaldo and Terai to characterize squarefree monomial ideals J with pd(R/J) ≤ μ(J) − 1, i.e. whose projective dimension equals the minimal number of generators of J minus 1. In this paper we prove sufficient and necessary combinatorial conditions for pd(R/J) ≤ μ(J)−2. The second main result is an effective explicit procedure to compute the projective...
متن کاملOn the VC-dimension of uniform hypergraphs
Let F be a k-uniform hypergraph on [n] where k − 1 is a power of some prime p and n ≥ n0(k). Our main result says that if |F | > ( n k−1 ) − logp n + k!kk , then there exists E0 ∈ F such that {E ∩ E0 : E ∈ F} contains all subsets of E0. This improves a longstanding bound of ( n k−1 ) due to Frankl and Pach [7].
متن کامل1 - Introduction to hypergraphs
We begin with an introduction to hypergraphs, which gives a taste of different representations of hypergraphs, linear hypergraphs, and Turán-type problems, including existence of Turán densities and classification of zero Turán densities. Thereafter we delve deeper into some of the classical theorems of hypergraph theory, including various theorems on intersecting families such as Sperner’s The...
متن کامل1-Sperner hypergraphs
We introduce a new class of hypergraphs, the class of 1-Sperner hypergraphs. A hypergraph H is said to be 1-Sperner if every two distinct hyperedges e, f of H satisfy min{|e \ f |, |f \ e|} = 1. We prove a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences, including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that e...
متن کامل1 Directed Hypergraphs and Applications ( * )
We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applica...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2017
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196717500291