Rainbow Connection Number and Independence Number of a Graph
نویسندگان
چکیده
منابع مشابه
Rainbow Connection Number of the Thorn Graph
A path in an edge colored graph is said to be a rainbow path if every edge in this path is colored with the same color. The rainbow connection number of G, denoted by rc(G), is the smallest number of colors needed to color its edges, so that every pair of its vertices is connected by at least one rainbow path. A rainbow u − v geodesic in G is a rainbow path of length d(u, v), where d(u, v) is t...
متن کاملRainbow Connection Number of Graph Power and Graph Products
The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. This graph parameter was introduced by Chartrand et al. in 2008. The problem has garnered considerable interest and several variants of the initial version have since been intr...
متن کاملRainbow Connection Number of Graph Power and Graph Products
Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (Note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely cartesian p...
متن کاملOriented diameter and rainbow connection number of a graph
The oriented diameter of a bridgeless graph G is min{diam(H) |H is an orientation of G}. A path in an edge-colored graph G, where adjacent edges may have the same color, is called rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every two distinct vertices of G are...
متن کاملRainbow Connection Number and Connectivity
The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) ≤ dn2 e for any 2-connected graph with at least three vertices. We conjecture that rc(G) ≤ n/κ + C for a κ-connected graph G of order n, w...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2016
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-016-1704-0