Colored Prüfer Codes for $k$-Edge Colored Trees

Colored Prüfer Codes for k-Edge Colored Trees

A combinatorial bijection between k-edge colored trees and colored Prüfer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)!(nk−n n−2 ) of k-edge colored trees with n vertices.

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...

Clustering on k-Edge-Colored Graphs

We study the Max k-colored clustering problem, where, given an edge-colored graph with k colors, we seek to color the vertices of the graph so as to find a clustering of the vertices maximizing the number (or the weight) of matched edges, i.e. the edges having the same color as their extremities. We show that the cardinality problem is NP-hard even for edge-colored bipartite graphs with a chrom...

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