Maximum colored trees in edge-colored graphs
نویسندگان
چکیده
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 and provide algorithms for graphs without properly edge-colored cycles. We also derive some nonapproximability bounds. A study of the trends random graphs display with regard to the presence of properly edge-colored spanning trees is presented.
منابع مشابه
Homomorphisms of 2-edge-colored graphs
In this paper, we study homomorphisms of 2-edge-colored graphs, that is graphs with edges colored with two colors. We consider various graph classes (outerplanar graphs, partial 2-trees, partial 3-trees, planar graphs) and the problem is to find, for each class, the smallest number of vertices of a 2-edge-colored graph H such that each graph of the considered class admits a homomorphism to H.
متن کاملColored 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 ...
متن کاملar X iv : 0 71 1 . 28 49 v 1 [ m at h . C O ] 1 9 N ov 2 00 7 Partitioning complete graphs by heterochromatic trees ∗
A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum positive integer p such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we determi...
متن کاملequi-bipartite graphs by monochromatic trees under a color degree condition
The monochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum integer k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. In general, to determine this number is very difficult. For 2-edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the ex...
متن کاملRainbow 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 )
متن کامل