منابع مشابه
On 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 کاملGraphs with Induced-Saturation Number Zero
Given graphs G and H, G is H-saturated if H is not a subgraph of G, but for all e / ∈ E(G), H appears as a subgraph of G + e. While for every n > |V (H)|, there exists an n-vertex graph that is H-saturated, the same does not hold for induced subgraphs. That is, there exist graphs H and values of n > |V (H)|, for which every n-vertex graph G either contains H as an induced subgraph, or there exi...
متن کاملSaturation 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 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 کاملThe Saturation Function of Complete Partite Graphs
A graph G is called F -saturated if it is F -free but the addition of any missing edge to G creates a copy of F . Let the saturation function sat(n, F ) be the minimum number of edges that an F -saturated graph on n vertices can have. We determine this function asymptotically for every fixed complete partite graph F as n tends to infinity and give some structural information about almost extrem...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.01.006