The B-Domatic Number of a Graph

  title={The B-Domatic Number of a Graph},
  author={Odile Favaron},
  booktitle={Discuss. Math. Graph Theory},
  • O. Favaron
  • Published in Discuss. Math. Graph Theory 1 September 2013
  • Mathematics
Abstract Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the… 
2 Citations

On the b-Domatic Number of Graphs

Some properties of b-Domatic partitions are explained, the minimum cardinality of a b-domatic partition of G is called the b- domatic number and is denoted by bd(G), and some families of graphs are determined.

Some new results on the b-domatic number of graphs

It is proved that for any graph G on n vertices, bd ( G )+ bd( Ġ ) ≤ n +1, where Ġ  is the complement of G.



The b-chromatic Number of a Graph

The achromatic number of a graph

On the b-Chromatic Number of Graphs

The b-chromatic number b(G) of a graph G = (V, E) is the largest integer k such that G admits a vertex partition into k independent sets Xi (i = 1, . . . , k) such that each Xi contains a vertex xi

On the b-chromatic number of regular graphs

The domatic number problem

A Characterization of b‐Perfect Graphs

It is proved that a graph is b-perfect if and only if it does not contain as an induced subgraph a member of a certain list of 22 graphs.

Upper bounds on the b-chromatic number and results for restricted graph classes

Four general upper bounds on the b-chromatic number χb(G) are established and it is proved that special graphs with disconnected graphs and graphs with independence number 2 are b-continuous.

Disjoint independent dominating sets in graphs

On Approximating the B-Chromatic Number