How many edge-colors for almost-rainbow K5s?
نویسنده
چکیده
Let f(n) be the minimum number of colors necessary to color the edges of Kn so that every path or cycle with four edges is at least three-colored. We show that f(n) ≥ 11 4 n − 23 4 improving on the bound of Axenovich for the generalized Ramsey number f(n, 5, 9) first studied by Erdös and Gyárfás. 2000 Mathematics Subject Classification: 05A15, 05C38, 05C55
منابع مشابه
How many randomly colored edges make a randomly colored dense graph rainbow hamiltonian or rainbow connected?
In this paper we study the randomly edge colored graph that is obtained by adding randomly colored random edges to an arbitrary randomly edge colored dense graph. In particular we ask how many colors and how many random edges are needed so that the resultant graph contains a fixed number of edge disjoint rainbow Hamilton cycles. We also ask when in the resultant graph every pair of vertices is ...
متن کاملRainbow Matching in Edge-Colored Graphs
A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident to v. Wang and Li conjectured that for k > 4, every edge-colored graph with minimum color degree at least k contains a rainbow matching of size at least ⌈k/2⌉. We prove the slightly weaker statement that a rainbow matching...
متن کاملRainbow numbers for small stars with one edge added
A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f(n, H) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of H . The rainbow number rb(n, H) is the minimum number of colors such that any edge-coloring of Kn with rb(n, H) number of colors contains a rainbow copy o...
متن کاملPaths and cycles with many colors in edge-colored complete graphs
In this paper we consider properly edge-colored complete graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A proper edge-coloring is a factorization if each color class is a perfect or near perfect matching. A subgraph is called rainbow if its edges have different colors. We show that in any factorization of the complete graph Kn on n vertic...
متن کاملA Rainbow k-Matching in the Complete Graph with r Colors
An r-edge-coloring of a graph is an assignment of r colors to the edges of the graph. An exactly r-edge-coloring of a graph is an r-edge-coloring of the graph that uses all r colors. A matching of an edge-colored graph is called rainbow matching, if no two edges have the same color in the matching. In this paper, we prove that an exactly r-edge-colored complete graph of order n has a rainbow ma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008