Decomposing 1-Sperner Hypergraphs
نویسندگان
چکیده
منابع مشابه
1-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 کاملdecomposing hypergraphs into k-colorable hypergraphs
for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.
متن کاملDecomposing Hypergraphs into Simple Hypertrees
Let T be a simple k-uniform hypertree with t edges. It is shown that if H is any k-uniform hypergraph with n vertices and with minimum degree at least n k−1 2k−1(k−1)! (1+o(1)), and the number of edges of H is a multiple of t then H has a T -decomposition. This result is asymptotically best possible for all simple hypertrees with at least two edges. Mathematics Subject Classification (1991): 05...
متن کاملDecomposing complete edge-chromatic graphs and hypergraphs
A d-graph G = (V ;E1, . . . , Ed) is a complete graph whose edges are colored by d colors, or in other words, are partitioned into d subsets (some of which might be empty). We say that G is complementary connected if the complement to each chromatic component of G is connected on V , or in other words, if for each two vertices u, w ∈ V and color i ∈ I = {1, . . . , d} there is a path between u ...
متن کاملPartitioning of Loop-free Sperner Hypergraphs into Transversals
This article explores possibilities of partitioning the vertex set of a given simple loop-free Sperner hypergraph into a union of transversals. Studies are done on the possible number of transversals in such partitions, followed by forming a hypergraph (on the vertex set of the given hypergraph) that consists of transversals for hyperedges. AMS Subject Classification: 05C65
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: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7890