On (Kt-e)-Saturated Graphs
نویسندگان
چکیده
Given a graph H, we say a graph G is H-saturated if G does not contain H as a subgraph and the addition of any edge e′ 6∈ E(G) results in H as a subgraph. In this paper, we construct (K4 − e)-saturated graphs with |E(G)| either the size of a complete bipartite graph, a 3-partite graph, or in the interval [ 2n− 4, ⌊ n 2 ⌋ ⌈ n 2 ⌉ − n+ 6 ] . We then extend the (K4−e)-saturated graphs to (Kt − e)-saturated graphs.
منابع مشابه
On Ramsey unsaturated and saturated graphs
A graph is Ramsey unsaturated if there exists a proper supergraph of the same order with the same Ramsey number, and Ramsey saturated otherwise. This has been studied by Balister, Lehel and Schelp [J. Graph Theory 51 (2006), 22–32]. In this paper, we show that some circulant graphs, trees with diameter 3, and Kt,n ∪ mK1 for infinitely many t, n and m, are Ramsey unsaturated.
متن کاملMinimum degree and the minimum size of Kt 2 - saturated graphs Ronald
A graph G is said to be F-saturated if G does not contain a copy of F as a subgraph and G+ e contains a copy of F as a subgraph for any edge e contained in the complement of G. Erdős et al. in [A problem in graph theory, Amer. Math. Monthly 71 (1964) 1107–1110.] determined the minimum number of edges, sat(n, F ), such that a graph G on n vertices must have when F is a t-clique. Later, Ollmann [...
متن کاملA Width Parameter Useful for Chordal and Co-comparability Graphs
In 2013 Belmonte and Vatshelle used mim-width, a graph parameter bounded on interval graphs and permutation graphs that strictly generalizes clique-width, to explain existing algorithms for many domination-type problems, also known as (σ, ρ)problems or LC-VSVP problems, on many special graph classes. In this paper, we focus on chordal graphs and co-comparability graphs, that strictly contain in...
متن کاملThe Edge Spectrum of K4-Saturated Graphs
Any H-free graph G is called H-saturated if the addition of any edge e / ∈ E(G) results in H as a subgraph of G. The minimum size of an H-saturated graph on n vertices is denoted by sat(n,H). The edge spectrum for the family of graphs with property P is the set of all sizes of graphs with property P . In this paper, we find the edge spectrum of K4-saturated graphs. We also show that if G is a K...
متن کاملSaturation numbers for families of graph subdivisions
For a family F of graphs, a graph G is F-saturated if G contains no member of F as a subgraph, but for any edge uv in G, G+ uv contains some member of F as a subgraph. The minimum number of edges in an F-saturated graph of order n is denoted sat(n,F). A subdivision of a graph H, or an H-subdivision, is a graph G obtained from H by replacing the edges of H with internally disjoint paths of arbit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 34 شماره
صفحات -
تاریخ انتشار 2018