Ramsey Numbers of Interval 2-Chromatic Ordered Graphs
نویسندگان
چکیده
منابع مشابه
Ramsey numbers of ordered graphs
An ordered graph G< is a graph G with vertices ordered by the linear ordering <. The ordered Ramsey number R(G<, c) is the minimum number N such that every ordered complete graph with c-colored edges and at least N vertices contains a monochromatic copy of G<. For unordered graphs it is known that Ramsey numbers of graphs with degrees bounded by a constant are linear with respect to the number ...
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Suppose G is a graph The chromatic Ramsey number rc G of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true For any colouring of the edges of F there is a monochromatic subgraph isomorphic to G Let Mn minfrc G G ng It was conjectured by S A Burr P Erd os and L Lov asz thatMn n This conjecture has been con rmed previously for n In this...
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Given a labeled graph H with vertex set {1, 2, . . . , n}, the ordered Ramsey number r<(H) is the minimum N such that every two-coloring of the edges of the complete graph on {1, 2, . . . , N} contains a copy of H with vertices appearing in the same order as in H. The ordered Ramsey number of a labeled graph H is at least the Ramsey number r(H) and the two coincide for complete graphs. However,...
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Let KN denote the complete graph on N vertices with vertex set V = V (KN ) and edge set E = E(KN ). For x, y ∈ V , let xy denote the edge between the two vertices x and y. Let L be any finite set and M ⊆ L3. Let c : E → L. Let [n] denote the integer set {1, 2, . . . , n}. For x, y, z ∈ V , let c(xyz) denote the ordered triple (c(xy), c(yz), c(xz)). We say that c is good with respect to M if the...
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An ordered graph is a pair G = (G,≺) where G is a graph and ≺ is a total ordering of its vertices. The ordered Ramsey number R(G) is the minimum number N such that every ordered complete graph with N vertices and with edges colored by two colors contains a monochromatic copy of G. We show that for every integer d ≥ 3, almost every d-regular graph G satisfies R(G) ≥ n3/2−1/d 4 log n log log n fo...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2019
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-019-02057-8