منابع مشابه
Saturation in random graphs
A graph H is Ks-saturated if it is a maximal Ks-free graph, i.e., H contains no clique on s vertices, but the addition of any missing edge creates one. The minimum number of edges in a Ks-saturated graph was determined over 50 years ago by Zykov and independently by Erdős, Hajnal and Moon. In this paper, we study the random analog of this problem: minimizing the number of edges in a maximal Ks-...
متن کاملOn the saturation number of graphs
Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...
متن کاملSaturation Numbers in Tripartite Graphs
Given graphs H and F , a subgraph G ⊆ H is an F -saturated subgraph of H if F * G, but F ⊆ G + e for all e ∈ E(H) \ E(G). The saturation number of F in H, denoted sat(H,F ), is the minimum number of edges in an F -saturated subgraph of H. In this paper we study saturation numbers of tripartite graphs in tripartite graphs. For ` ≥ 1 and n1, n2, and n3 sufficiently large, we determine sat(Kn1,n2,...
متن کاملRandom Trees in Random Graphs
We show that a random labeled n-vertex graph almost surely contains isomorphic copies of almost all labeled n-vertex trees, in two senses. In the first sense, the probability of each edge occurring in the graph diminishes as n increases, and the set of trees referred to as "almost all" depends on the random graph. In the other sense, the probability of an edge occurring is fixed, and the releva...
متن کاملHoles in random graphs
tuczak, T., Holes in random graphs, Discrete Applied Mathematics 30 (1991) 213-219. It is shown that for every E>O with the probability tending to 1 as n-00 a random graph G(n,p) contains induced cycles of all lengths k, 3 <k~ (1 &)n log C/C, provided c(n) = (n l)p(n)-a.
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2016
ISSN: 1042-9832
DOI: 10.1002/rsa.20703