decomposing hypergraphs into k-colorable hypergraphs
نویسندگان
چکیده
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 $lceil log_{k} chi(h) rceil$.
منابع مشابه
Decomposing 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 کاملOn decomposing a hypergraph into k connected sub-hypergraphs
By applying the matroid partition theorem of J. Edmonds [1] to a hypergraphic generalization of graphic matroids, due to M. Lorea [3], we obtain a generalization of Tutte’s disjoint trees theorem for hypergraphs. As a corollary, we prove for positive integers k and q that every (kq)-edge-connected hypergraph of rank q can be decomposed into k connected sub-hypergraphs, a well-known result for q...
متن کاملUniquely colorable mixed hypergraphs
A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, χ̄ and χ, respectively. A mixed hypergraph is called uniquely colo...
متن کاملOrderings of uniquely colorable hypergraphs
For a mixed hypergraphH= (X,C,D), where C andD are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’such that everyC ∈ Cmeets some class in more than one vertex, and everyD ∈ D has a nonempty intersection with at least two classes.A vertex-order x1, x2, . . . , xn onX (n=|X|) is uniquely colorable if the subhypergraph induced by {xj : 1 j i} has precisely on...
متن کاملDecomposing complete 3-uniform hypergraphs into Hamiltonian cycles
Using the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph, we continue the investigation of the existence of a decomposition of the complete 3-uniform hypergraph into Hamiltonian cycles began by Bailey and Stevens. We also discuss two extensions of the problem: to the complete 3-uniform hypergraph from which a parallel class of triples has been removed, and to the com...
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 کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
transactions on combinatoricsناشر: university of isfahan
ISSN 2251-8657
دوره 3
شماره 2 2014
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023