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276
On the rainbow kconnectivity of complete graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 49 (2011), PAGES 217–226
, 2011
"... A path in an edgecolored graph G, where adjacent edges may be colored the same, is called a rainbow path if no two edges of the path are colored the same. For a κconnected graph G and an integer k with 1 ≤ k ≤ κ, the rainbow kconnectivity rck(G)ofG is defined as the minimum integer j for which th ..."
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Cited by 1 (1 self)
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A path in an edgecolored graph G, where adjacent edges may be colored the same, is called a rainbow path if no two edges of the path are colored the same. For a κconnected graph G and an integer k with 1 ≤ k ≤ κ, the rainbow kconnectivity rck(G)ofG is defined as the minimum integer j for which
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
On Rainbow Coloring of Some Classes of Graphs
, 2012
"... A path in an edge colored graph is said to be a rain bow path if no two edges on the path have the same color. An edge colored graph is rainbow connected if there exists a rainbow path between every pair of vertices. The rainbow connectivity of a graph G, denoted by rc(G) is the smallest number of c ..."
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of colors required to edge color the graph such that the graph is rainbow connected. In this paper a rainbow coloring of the corona of Pn οK2the corona of PnºC4,flower graphs and fan graph are considered and rc(G) of these graphs are decided.
On the Total k Diameter of Connection Networks
, 1997
"... We study connection networks in which certain pairs of nodes have to be connected by k edgedisjoint paths, and study bounds for the minimal sum of lengths of such k paths. We define the related notions of total k distance for a pair of nodes and total k diameter of a connection network, and study ..."
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Cited by 1 (0 self)
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We study connection networks in which certain pairs of nodes have to be connected by k edgedisjoint paths, and study bounds for the minimal sum of lengths of such k paths. We define the related notions of total k distance for a pair of nodes and total k diameter of a connection network
Rainbow Connectivity: Hardness and Tractability
 IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS
, 2011
"... A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (sr ..."
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Cited by 6 (0 self)
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A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted
Oriented diameter and rainbow connection number of a graph
, 2014
"... The oriented diameter of a bridgeless graph G is min{diam(H)  H is a strang orientation of G}. A path in an edgecolored 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 smalle ..."
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is the smallest integer number k for which there exists a kedgecoloring of G such that every two distinct vertices of G are connected by a rainbow path. In this paper, we obtain upper bounds for the oriented diameter and the rainbow connection number of a graph in terms of rad(G) and η(G), where rad
Results 1  10
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276