منابع مشابه
Monochromatic Boxes in Colored Grids
A d-dimensional grid is a set of the form L 1⁄4 1⁄2a1 × · · · ×1⁄2ad , where 1⁄2t 1⁄4 f1; : : : ; tg and aj is a positive integer for j ∈ 1⁄2d . A d-dimensional box is a set of the form fx1; y1g× · · · ×fxd; ydg for some integers xj, yj with j ∈ 1⁄2d , where xj ≠ yj for each j. We give conditions on the set of d-tuples ða1; : : : ; adÞ so that, for every coloring f : L → 1⁄2c , the grid L 1⁄4 1...
متن کاملMonochromatic cycles and monochromatic paths in arc-colored digraphs
We call the digraph D an m-colored digraph if the arcs of D are colored with m colors. A path (or a cycle) is called monochromatic if all of its arcs are colored alike. A cycle is called a quasi-monochromatic cycle if with at most one exception all of its arcs are colored alike. A subdigraph H in D is called rainbow if all its arcs have different colors. A set N ⊆ V (D) is said to be a kernel b...
متن کاملMonochromatic triangles in two-colored plane
We prove that for any partition of the plane into a closed set C and an open set O and for any configuration T of three points, there is a translated and rotated copy of T contained in C or in O. Apart from that, we consider partitions of the plane into two sets whose common boundary is a union of piecewise linear curves. We show that for any such partition and any configuration T which is a ve...
متن کاملMonochromatic cycle partitions of edge-colored graphs
In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G)= . Generalizing a classical conjecture of Erd” os, Gyárfás and Pyber, we conjecture that if we r -color the edges of a graph G with (G)= , then the vertex set of G can be partitioned into at most r vertex disjoint monochromatic cycles. In the direct...
متن کاملMonochromatic subgraphs of 2-edge-colored graphs
Lehel conjectured that for all n, any 2-edge-coloring of Kn admits a partition of the vertex set into a red cycle and a blue cycle. This conjecture led to a significant amount of work on related questions and was eventually proven for all n by Bessy and Thomassé. Balogh, Barát, Gerbner, Gyárfás, and Sárközy conjectured a stronger statement for large n: that if δ(G) > 3n/4, then any 2-edge-color...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/080740702