排序方式: 共有135条查询结果,搜索用时 31 毫秒
51.
A 3‐uniform hypergraph (3‐graph) is said to be tight, if for any 3‐partition of its vertex set there is a transversal triple. We give the final steps in the proof of the conjecture that the minimum number of triples in a tight 3‐graph on n vertices is exactly . © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 103–114, 2007 相似文献
52.
Benjamin Doerr 《Proceedings of the American Mathematical Society》2004,132(7):1905-1912
We investigate the discrepancy (or balanced coloring) problem for hypergraphs and matrices in arbitrary numbers of colors. We show that the hereditary discrepancy in two different numbers of colors is the same apart from constant factors, i.e.,
This contrasts the ordinary discrepancy problem, where no correlation exists in many cases.
This contrasts the ordinary discrepancy problem, where no correlation exists in many cases.
53.
Matěj Stehlík 《Graphs and Combinatorics》2006,22(3):421-426
A hypergraph is τ-critical if τ(−{E})<τ() for every edge E ∈ , where τ() denotes the transversal number of . We show that if is a connected τ-critical hypergraph, then −{E} can be partitioned into τ()−1 stars of size at least two, for every edge E ∈ . An immediate corollary is that a connected τ-critical hypergraph has at least 2τ()−1 edges. This extends, in a very natural way, a classical theorem of Gallai on colour-critical graphs, and is equivalent
to a theorem of Füredi on t-stable hypergraphs. We deduce a lower bound on the size of τ-critical hypergraphs of minimum degree at least two. 相似文献
55.
The size‐Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2‐edge‐coloring of H yields a monochromatic copy of G. Size‐Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size‐Ramsey numbers for k‐uniform hypergraphs. Analogous to the graph case, we consider the size‐Ramsey number of cliques, paths, trees, and bounded degree hypergraphs. Our results suggest that size‐Ramsey numbers for hypergraphs are extremely difficult to determine, and many open problems remain. 相似文献
56.
Answering in a strong form a question posed by Bollobás and Scott, in this paper we determine the discrepancy between two random k‐uniform hypergraphs, up to a constant factor depending solely on k. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 47, 147–162, 2015 相似文献
57.
Wiebke Bedenknecht Jie Han Yoshiharu Kohayakawa Guilherme O. Mota 《Random Structures and Algorithms》2019,55(4):795-807
For k ≥ 2 and r ≥ 1 such that k + r ≥ 4, we prove that, for any α > 0, there exists ε > 0 such that the union of an n‐vertex k‐graph with minimum codegree and a binomial random k‐graph with on the same vertex set contains the rth power of a tight Hamilton cycle with high probability. This result for r = 1 was first proved by McDowell and Mycroft. 相似文献
58.
We introduce a new approach and prove that the maximum number of triangles in a -free graph on vertices is at most We show a connection to -uniform hypergraphs without (Berge) cycles of length less than six, and estimate their maximum possible size. Using our approach, we also (slightly) improve the previous estimate on the maximum size of an induced--free and -free graph. 相似文献
59.
Beka Ergemlidze 《Discrete Mathematics》2021,344(4):112262
In this paper, we consider maximum possible value for the sum of cardinalities of hyperedges of a hypergraph without a Berge 4-cycle. We significantly improve the previous upper bound provided by Gerbner and Palmer. Furthermore, we provide a construction that slightly improves the previous lower bound. 相似文献
60.
For positive integers r>?, an r‐uniform hypergraph is called an ?‐cycle if there exists a cyclic ordering of its vertices such that each of its edges consists of r consecutive vertices, and such that every pair of consecutive edges (in the natural ordering of the edges) intersect in precisely ? vertices; such cycles are said to be linear when ?=1, and nonlinear when ?>1. We determine the sharp threshold for nonlinear Hamiltonian cycles and show that for all r>?>1, the threshold for the appearance of a Hamiltonian ?‐cycle in the random r‐uniform hypergraph on n vertices is sharp and given by for an explicitly specified function λ. This resolves several questions raised by Dudek and Frieze in 2011.10 相似文献