Opuscula Math. 33, no. 1 (2013), 19-28
On vertex b-critical trees
Abstract. A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that has neighbors of all other colors. The b-chromatic number of a graph \(G\) is the largest \(k\) such that \(G\) admits a b-coloring with \(k\) colors. A graph \(G\) is b-critical if the removal of any vertex of \(G\) decreases the b-chromatic number. We prove various properties of b-critical trees. In particular, we characterize b-critical trees.
Keywords: b-coloring, b-critical graphs, b-critical trees.
Mathematics Subject Classification: 05C15.
- Received: 2011-05-09.
- Revised: 2012-03-08.
- Accepted: 2012-09-18.