منابع مشابه
Decompositions of edge-colored infinite complete graphs into monochromatic paths
For r ∈ N\{0} an r-edge coloring of a graph or hypergraph G = (V,E) is a map c : E → {0, . . . , r−1}. Extending results of Rado and answering questions of Rado, Gyárfás and Sárközy we prove that • every r-edge colored complete k-uniform hypergraph on N can be partitioned into r monochromatic tight paths with distinct colors (a tight path in a kuniform hypergraph is a sequence of distinct verti...
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Let l and k be positive integers, and let X = {0, 1, . . . , l}. Is it true that for every coloring δ : X × X → {0, 1, . . .} there either exist elements x0 < x1 < . . . < xl of X with δ(x0, x1) = δ(x1, x2) = . . . = δ(xl−1, xl), or else there exist elements y0 < y1 < . . . < yk of X with δ(yi−1, yi) 6= δ(yj−1, yj) for all 1 ≤ i < j ≤ k? We prove here that this is the case if either l ≤ 2, or k...
متن کاملMonochromatic paths and monochromatic sets of arcs in bipartite tournaments
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours and all of them are used. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices there is no monochromatic path between them and for every vertex v in V (D) \ N there is a monochromatic p...
متن کاملMonochromatic Paths and Triangulated Graphs
This paper considers two properties of graphs, one geometrical and one topolog-ical, and shows that they are strongly related. Let G be a graph with four distinguished and distinct vertices, w 1 ; w 2 ; b 1 ; b 2. Consider the two properties, T RI + (G) and M ON O(G), deened as follows. T RI + (G): There is a planar drawing of G such that: all 3-cycles of G are faces; all faces of G are triangl...
متن کاملMonochromatic paths in random tournaments
We prove that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ log n). This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7758