| http://dbpedia.org/ontology/abstract
|
In graph theory, a rainbow-independent set … In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following conditions:
* It is an independent set – every two vertices in U are not adjacent (there is no edge between them);
* It is a rainbow set – U contains at most a single vertex from each color Vi. Other terms used in the literature are independent set of representatives, independent transversal, and independent system of representatives. As an example application, consider a faculty with m departments, where some faculty members dislike each other. The dean wants to construct a committee with m members, one member per department, but without any pair of members who dislike each other. This problem can be presented as finding an ISR in a graph in which the nodes are the faculty members, the edges describe the "dislike" relations, and the subsets V1, …, Vm are the departments.the subsets V1, …, Vm are the departments.
|
| rdfs:comment |
In graph theory, a rainbow-independent set … In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following conditions:
* It is an independent set – every two vertices in U are not adjacent (there is no edge between them);
* It is a rainbow set – U contains at most a single vertex from each color Vi.t most a single vertex from each color Vi.
|
