Results 1  10
of
304,872
Bipartite, Colorable and Colored Graphs
, 2003
"... A labeled graph is bipartite if its vertex set can be partitioned into two disjoint subsets and , = ∪, such that every edge of is of the form ( ), where ∈ and ∈ . Let be a positive integer and = {1 2 }. A labeled graph is colorable if there exists a function → with t ..."
Abstract
 Add to MetaCart
A labeled graph is bipartite if its vertex set can be partitioned into two disjoint subsets and , = ∪, such that every edge of is of the form ( ), where ∈ and ∈ . Let be a positive integer and = {1 2 }. A labeled graph is colorable if there exists a function
On the Uniquely List Colorable Graphs
 ARS COMBIN
, 2001
"... Let G be a graph with vertices, and let S 1 ; S 2 ; : : : ; S be a list of colors on its vertices, each of size k. If there exists a unique proper coloring for G from this list of colors, then G is called uniquely klist colorable graph. We characterize all uniquely 2list colorable graphs, an ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Let G be a graph with vertices, and let S 1 ; S 2 ; : : : ; S be a list of colors on its vertices, each of size k. If there exists a unique proper coloring for G from this list of colors, then G is called uniquely klist colorable graph. We characterize all uniquely 2list colorable graphs
Paths and cycles in colored graphs
 Australasian J. Combin
"... Let G be an (edge)colored graph. A path (cycle) is called monochromatic if all of its edges have the same color, and is called heterochromatic if all of its edges have different colors. In this paper, some sufficient conditions for the existence of (long) monochromatic paths and cycles, and those f ..."
Abstract

Cited by 23 (9 self)
 Add to MetaCart
Let G be an (edge)colored graph. A path (cycle) is called monochromatic if all of its edges have the same color, and is called heterochromatic if all of its edges have different colors. In this paper, some sufficient conditions for the existence of (long) monochromatic paths and cycles, and those
Randomly coloring graphs and coloring random graphs.
"... Abstract Randomly coloring graphs and coloring random graphs. ..."
Balance Games on Colored Graphs
"... Abstract. We consider games played on finite colored graphs for an infinite number of rounds, whose goal is to visit all colors with the same asymptotic frequency. Such games may represent scheduling problems with special fairness constraints. We show that the main corresponding decision problems ar ..."
Abstract
 Add to MetaCart
Abstract. We consider games played on finite colored graphs for an infinite number of rounds, whose goal is to visit all colors with the same asymptotic frequency. Such games may represent scheduling problems with special fairness constraints. We show that the main corresponding decision problems
Links in edgecolored graphs
 European J. Combin
"... A graph is klinked (kedgelinked), k ≥ 1, if for each k pairs of vertices x1, y1, · · · , xk, yk, there exist k pairwise vertexdisjoint (respectively edgedisjoint) paths, one per pair xi and yi, i = 1, 2, · · · , k. Here we deal with the properlyedgecolored version of the klinked (kedge ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
A graph is klinked (kedgelinked), k ≥ 1, if for each k pairs of vertices x1, y1, · · · , xk, yk, there exist k pairwise vertexdisjoint (respectively edgedisjoint) paths, one per pair xi and yi, i = 1, 2, · · · , k. Here we deal with the properlyedgecolored version of the k
Colored graphs without colorful cycles
"... A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a colored graph lacks colorful cycles iff it is Gallai, i.e., lacks colorful triangles. We then show that, under the oper ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a colored graph lacks colorful cycles iff it is Gallai, i.e., lacks colorful triangles. We then show that, under
The canonical coloring graph of trees and cycles
 Ars Mathematica Contemporanea
, 2012
"... For a graph G and an ordering of the vertices pi, the set of canonical kcolorings of G under pi is the set of nonisomorphic proper kcolorings ofG that are lexicographically least under pi. The canonical coloring graph Canpik (G) is the graph with vertex set the canonical colorings of G and two ve ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
For a graph G and an ordering of the vertices pi, the set of canonical kcolorings of G under pi is the set of nonisomorphic proper kcolorings ofG that are lexicographically least under pi. The canonical coloring graph Canpik (G) is the graph with vertex set the canonical colorings of G and two
Random Walks on Colored Graphs
 Random Struct. Alg
, 1994
"... We initiate a study of random walks on undirected graphs with colored edges. In our model, a sequence of colors is specified before the walk begins, and it dictates the color of edge to be followed at each step. We give tight upper and lower bounds on the expected cover time of a random walk on an u ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We initiate a study of random walks on undirected graphs with colored edges. In our model, a sequence of colors is specified before the walk begins, and it dictates the color of edge to be followed at each step. We give tight upper and lower bounds on the expected cover time of a random walk
Results 1  10
of
304,872