Extremality of graph entropy based on degrees of uniform hypergraphs with few edges
نویسندگان
چکیده
Let H be a hypergraph with n vertices. Suppose that d1, d2, . . . , dn are degrees of the vertices of H. The t-th graph entropy based on degrees of H is defined as
منابع مشابه
ENTROPY OF DYNAMICAL SYSTEMS ON WEIGHTS OF A GRAPH
Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, t...
متن کاملAsymptotic Enumeration of Sparse Uniform Linear Hypergraphs with Given Degrees
A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For n ≥ 3, let r = r(n) ≥ 3 be an integer and let k = (k1, . . . , kn) be a vector of nonnegative integers, where each kj = kj(n) may depend on n. Let M = M(n) = ∑n j=1 kj for all n ≥ 3, and define the set I = {n ≥ 3 | r(n) divides ...
متن کاملConflict-free Colorings of Uniform Hypergraphs with Few Edges
A coloring of the vertices of a hypergraph H is called conflict-free if each edge e of H contains a vertex whose color does not repeat in e. The smallest number of colors required for such a coloring is called the conflict-free chromatic number of H, and is denoted by χCF (H). Pach and Tardos proved that for an (2r − 1)-uniform hypergraph H with m edges, χCF (H) is at most of the order of rm lo...
متن کاملOn Tours that Contain All Edges of a Hypergraph
Let H be a k-uniform hypergraph, k > 2. By an Euler tour in H we mean an alternating sequence v0, e1, v1, e2, v2, . . . , vm−1, em, vm = v0 of vertices and edges in H such that each edge of H appears in this sequence exactly once and vi−1, vi ∈ ei, vi−1 6= vi, for every i = 1, 2, . . . ,m. This is an obvious generalization of the graph theoretic concept of an Euler tour. A straightforward neces...
متن کاملShort paths in 3-uniform quasi-random hypergraphs
Frankl and Rödl [3] proved a strong regularity lemma for 3-uniform hypergraphs, based on the concept of δ-regularity with respect to an underlying 3-partite graph. In applications of that lemma it is often important to be able to “glue” together separate pieces of the desired subhypergraph. With this goal in mind, in this paper it is proved that every pair of typical edges of the underlying gra...
متن کامل