Sufficient conditions for the existence of spanning colored trees in edge-colored graphs

Sufficient conditions for the existence of spanning colored trees in edge-colored graphs

Colored Trees in Edge-Colored Graphs

The study of problems modeled by edge-colored graphs has given rise to important developments during the last few decades. For instance, the investigation of spanning trees for graphs provide important and interesting results both from a mathematical and an algorithmic point of view (see for instance [1]). From the point of view of applicability, problems arising in molecular biology are often ...

Maximum colored trees in edge-colored graphs

Abstract We consider maximum properly edge-colored trees in edge-colored graphs Gc. We also consider the problem where, given a vertex r, determine whether the graph has a spanning tree rooted at r, such that all root-to-leaf paths are properly colored. We consider these problems from graphtheoretic as well as algorithmic viewpoints. We prove their optimization versions to be NP-hard in general...

Multi-colored Spanning Graphs

We study a problem proposed by Hurtado et al. [10] motivated by sparse set visualization. Given n points in the plane, each labeled with one or more primary colors, a colored spanning graph (CSG) is a graph such that for each primary color, the vertices of that color induce a connected subgraph. The Min-CSG problem asks for the minimum sum of edge lengths in a colored spanning graph. We show th...

Sufficient Conditions for the Existence of Perfect Heterochromatic Matchings in Colored Graphs

Let G = (V, E) be an (edge-)colored graph, i.e., G is assigned a mapping C : E → {1, 2, · · · , r}, the set of colors. A matching of G is called heterochromatic if its any two edges have different colors. Unlike uncolored matchings for which the maximum matching problem is solvable in polynomial time, the maximum heterochromatic matching problem is NP-complete. This means that to find both suff...