On the Set of Simple Hypergraph Degree Sequences
نویسنده
چکیده
For a given m, 0 < m ≤ 2, let Dm(n) denote the set of all hypergraphic sequences for hypergraphs with n vertices and m hyperedges. A hypergraphic sequence in Dm(n) is upper hypergraphic if all its components are at least m/2. Let ?̂?m(n) denote the set of all upper hypergraphic sequences. A structural characterization of the lowest and highest rank maximal elements of ?̂?m(n) was provided in an earlier study. In the current paper we present an analogous characterization for all upper non-hypergraphic sequences. This allows determining the thresholds ?̅?min and rmax such that all upper sequences of ranks lower than ?̅?min are hypergraphic and all sequences of ranks higher than rmax are non-hypergraphic.
منابع مشابه
Nonconvexity of the Set of Hypergraph Degree Sequences
It is well known that the set of possible degree sequences for a simple graph on n vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequences for a simple k-uniform hypergraph on n vertices is not the intersection of a lattice and a convex polytope for k > 3 and n > k + 13. We also show an analogous nonconvexity result for the set of degre...
متن کاملRealizing degree sequences with k-edge-connected uniform hypergraphs
An integral sequence d = (d1, d2, . . . , dn) is hypergraphic if there is a simple hypergraph H with degree sequence d, and such a hypergraph H is a realization of d. A sequence d is r-uniform hypergraphic if there is a simple r-uniform hypergraph with degree sequence d. Similarly, a sequence d is r-uniformmulti-hypergraphic if there is an r-uniformhypergraph (possibly with multiple edges) with...
متن کاملOD-characterization of Almost Simple Groups Related to displaystyle D4(4)
Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident...
متن کاملCyclic Hypergraph Degree Sequences
The problem of efficiently characterizing degree sequences of simple hypergraphs is a fundamental long-standing open problem in Graph Theory. Several results are known for restricted versions of this problem. This paper adds to the list of sufficient conditions for a degree sequence to be hypergraphic. This paper proves a combinatorial lemma about cyclically permuting the columns of a binary ta...
متن کاملDegree Sequences in Complexes and Hypergraphs
Given an rc-complex K and a vertex v in K, the ndegree of v is the number of n-simplexes in K containing t7. The set of all Ti-degrees in a complex K is called its n-degree sequence when arranged in nonincreasing order. The question "Which sequences of integers are ndegree sequences?" is answered in this paper. This is done by generalizing the iterative characterization for the 1-dimensional (g...
متن کامل