Multi-colored spanning graphs

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...

Colored Spanning Graphs for Set Visualization

We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting...

Rainbow spanning subgraphs of edge-colored complete graphs

Consider edge-colorings of the complete graph Kn. Let r(n, t) be the maximum number of colors in such a coloring that does not have t edge-disjoint rainbow spanning trees. Let s(n, t) be the maximum number of colors in such a coloring having no rainbow spanning subgraph with diameter at most t. We prove r(n, t) = (n−2 2 )

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...

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