The rainbow connection number of 2-connected graphs
نویسندگان
چکیده
The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most dn/2e. The bound is optimal.
منابع مشابه
Rainbow connection in oriented graphs
An edge-coloured graph G is said to be rainbow-connected if any two vertices are connected by a path whose edges have different colours. The rainbow connection number of a graph is the minimum number of colours needed to make the graph rainbow-connected. This graph parameter was introduced by G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang in 2008. Since, the topic drew much attention, and v...
متن کاملVertex rainbow colorings of graphs
In a properly vertex-colored graphG, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P . If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring ofG. The minimum numbe...
متن کاملComputing Minimum Rainbow and Strong Rainbow Colorings of Block Graphs
A path in an edge-colored graph G is rainbow if no two edges of it are colored the same. The graph G is rainbow-connected if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph G is strongly rainbow-connected. The minimum number of colors needed to make G rainbow-connected is known as the rainbow connection number...
متن کاملOn Rainbow Connection Number and Connectivity
Rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we investigate the relationship of rainbow connection number with vertex and edge connectivity. It is already known that for a connected graph with minimum...
متن کاملRainbow connections for outerplanar graphs with diameter 2 and 3
An edge-colored graph G is rainbow connected if every two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rcðGÞ, is the smallest number of colors that are needed in order to make G rainbow connected. It was proved that computing rcðGÞ is an NP-hard problem, as well as that even deciding whether a graph has rcðGÞ...
متن کاملOn forbidden subgraphs and rainbow connection in graphs with minimum degree 2
A connected edge-colored graphG is said to be rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors, and the rainbow connection number rc(G) ofG is the minimum number of colors that can make G rainbow-connected. We consider families F of connected graphs for which there is a constant kF such that every connected F-free graph G with...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 313 شماره
صفحات -
تاریخ انتشار 2013