Least resolved trees for two-colored best match 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...

Building Graphs from Colored Trees

We will explore the computational complexity of satisfying certain sets of neighborhood conditions in graphs with various properties. More precisely, fix a radius ρ and let N(G) be the set of isomorphism classes of ρ-neighborhoods of vertices of G where G is a graph whose vertices are colored (not necessarily properly) by colors from a fixed finite palette. The root of the neighborhood will be ...

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

Rainbow spanning trees in complete graphs colored by one-factorizations

Brualdi and Hollingsworth conjectured that, for even n, in a proper edge coloring of Kn using precisely n − 1 colors, the edge set can be partitioned into n2 spanning trees which are rainbow (and hence, precisely one edge from each color class is in each spanning tree). They proved that there always are two edge disjoint rainbow spanning trees. Kaneko, Kano and Suzuki improved this to three edg...