| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 420040 | Discrete Applied Mathematics | 2013 | 20 Pages |
A b-colouring of a graph is a colouring of its vertices such that every colour class contains a vertex that has a neighbour in all other classes. The b-chromatic number of a graph is the largest integer kk such that the graph has a b-colouring with kk colours. We show how to find in polynomial time an optimal b-colouring of the Cartesian product of trees by paths, cycles and stars.
► We give polynomial time algorithm for computing the b-chromatic number of the Cartesian product of a tree by a Pk,k>4Pk,k>4. ► We give polynomial time algorithm for computing the b-chromatic number of the Cartesian product of a tree by a Ck,k>3Ck,k>3. ► We give polynomial time algorithm for computing the b-chromatic number of the Cartesian product of a tree by a star. ► We give general ideas of how to treat the Cartesian product of a tree by any other graph.
