منابع مشابه
Weak saturation numbers for multiple copies
For a fixed graph F , a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F inG+e. Theminimumnumber of edges in an F-saturated graph of order nwill be denoted by sat(n, F). A graph G is weakly F-saturated if G contains no copy of F and there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a ...
متن کاملWeak saturation numbers for sparse graphs
For a fixed graph F , a graph G is F -saturated if there is no copy of F in G, but for any edge e 6∈ G, there is a copy of F in G+ e. The minimum number of edges in an F -saturated graph of order n will be denoted by sat(n, F ). A graph G is weakly F -saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F . Th...
متن کاملSaturation Numbers of Books
A book Bp is a union of p triangles sharing one edge. This idea was extended to a generalized book Bb,p, which is the union of p copies of a Kb+1 sharing a common Kb. A graph G is called an H-saturated graph if G does not contain H as a subgraph, but G∪ {xy} contains a copy of H, for any two nonadjacent vertices x and y. The saturation number of H, denoted by sat(H,n), is the minimum number of ...
متن کاملSaturation Numbers for Trees
For a fixed graph H, a graph G is H-saturated if there is no copy of H in G, but for any edge e 6∈ G, there is a copy of H in G + e. The collection of Hsaturated graphs of order n is denoted by SAT(n,H), and the saturation number, sat(n,H), is the minimum number of edges in a graph in SAT(n,H). Let Tk be a tree on k vertices. The saturation numbers sat(n, Tk) for some families of trees will be ...
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,...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2019
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2019.04.003