Dirac-Type Conditions for Spanning Bounded-Degree Hypertrees
نویسندگان
چکیده
We prove that for fixed k, every k-uniform hypergraph on n vertices and of minimum codegree at least \(n/2+o(n)\) contains spanning tight k-tree bounded vertex degree as a subgraph. This generalises well-known result Komlos, Sarkozy Szemeredi graphs. Our is asymptotically sharp .
منابع مشابه
Degree Bounded Spanning Trees
In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set S ⊆ V(G) of cardinality n(k − 1) + c + 2, there exists a vertex set X ⊆ S of cardinality k such that the degree sum of vertices in X is at least |V(G)| − c − 1. Then G has a spanning tree T with maximum de...
متن کاملDegree Conditions for Spanning Brooms
A broom is a tree obtained by subdividing one edge of the star an arbitrary number of times. In [E. Flandrin, T. Kaiser, R. Kužel, H. Li and Z. Ryjáček, Neighborhood Unions and Extremal Spanning Trees, Discrete Math. 308 (2008), 2343-2350] Flandrin et al. posed the problem of determining degree conditions that ensure a connected graph G contains a spanning tree that is a broom. In this paper, w...
متن کاملDegree-bounded minimum spanning trees
* to be exact, times the weight of a minimum spanning tree (MST). In particular, we present an improved analysis of Chan’s degree-4 MST algorithm [4]. Previous results. Arora [1] and Mitchell [9] presented PTASs for TSP in Euclidean metric, for fixed dimensions. Unfortunately, neither algorithm extends to find degree-3 or degree-4 trees. Recently, Arora and Chang [3] have devised a quasi-polyno...
متن کاملSpanning Trees of Bounded Degree
Dirac’s classic theorem asserts that if G is a graph on n vertices, and δ(G) ≥ n/2, then G has a hamilton cycle. As is well known, the proof also shows that if deg(x) + deg(y) ≥ (n− 1), for every pair x, y of independent vertices in G, then G has a hamilton path. More generally, S. Win has shown that if k ≥ 2, G is connected and ∑ x∈I deg(x) ≥ n− 1 whenever I is a k-element independent set, the...
متن کاملMaximum number of colors in hypertrees of bounded degree
The upper chromatic number χ(H) of a hypergraph H = (X, E) is the maximum number of colors that can occur in a vertex coloring φ : X → N such that no edge E ∈ E is completely multicolored. A hypertree (also called arboreal hypergraph) is a hypergraph whose edges induce subtrees on a fixed tree graph. It has been shown that on hypertrees it is algorithmically hard not only to determine exactly b...
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: Trends in mathematics
سال: 2021
ISSN: ['2297-024X', '2297-0215']
DOI: https://doi.org/10.1007/978-3-030-83823-2_94