منابع مشابه
Ramsey-minimal graphs for star-forests
It is shown that if G and H are star-forests with no single edge stars, then (G, H) is Ramsey-finite if and only if both G and H are single stars with an odd number of edges . Further (5,,, U kS 1 , S, U 1S T ) is Ramsey-finite when m and n are odd, where S, denotes a star with i edges . In general, for G and H star-forests, (G U kS i , H U lS,) can be shown to be Ramsey-finite or Ramsey-infini...
متن کاملRamsey-minimal graphs for forests
It is shown in this paper that the pair (G, H) is Ramsey infinite when both G and H are forests, with at least one of G or H having a non-star component. In addition, an infinite subfamily of R(PP.) is constructed .
متن کاملAll Ramsey (2K2,C4)−Minimal Graphs
Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...
متن کاملMinimal Ordered Ramsey Graphs
An ordered graph is a graph equipped with a linear ordering of its vertex set. A pair of ordered graphs is Ramsey finite if it has only finitely many minimal ordered Ramsey graphs and Ramsey infinite otherwise. Here an ordered graph F is an ordered Ramsey graph of a pair (H,H ′) of ordered graphs if for any coloring of the edges of F in colors red and blue there is either a copy of H with all e...
متن کاملOn Ramsey Minimal Graphs
An elementary probabilistic argument is presented which shows that for every forest F other than a matching, and every graph G containing a cycle, there exists an infinite number of graphs J such that J → (F,G) but if we delete from J any edge e the graph J − e obtained in this way does not have this property. Introduction. All graphs in this note are undirected graphs, without loops and multip...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90266-1