… the previous lemmas since we are interested in graphs with girth at least 7. In the next …
, given a graph G with girth at least 7 that has a good set, we construct a b-coloring of G with …

… graphs with high girth have high b-chromatic number when compared to m(G). Here, we prove
that every graph with girth at … results related to reducing the girth requirement of our proof. …

… A b-coloring of the vertices of a graph is a proper coloring where each color class contains
a … G has a b-coloring with b(G) colors. A graph G is b-continuous if G has a b-coloring with k …

… b-continuity of a graph G is to modify a b-coloring of G with k colors in order to obtain a b-coloring
with \(k-1\) colors. We mention that obtaining just any b-coloring of a graph G is an easy …

… We mention that, if G is a bipartite graph with girth at least 6 and a b-coloring of G with k colors
is given, k ≥ χ(G)+1, then, with a little more work, one can get from the proof of Lemma 3.1 …

… We noticed that, if G is a bipartite graph with girth at least 6 and a b-coloring of G with k colors
is given, with k ≥ χ ( G ) + 1 , then, with a little more work in the proof of Lemma 2, one can …

… we prove that if G has a b-coloring with k colors and k ≥ χ(G) + 2, then either we can construct
a … Additionally, given the interest in regular graphs and bipartite graphs with large girth, we …

… P4-sparse graphs and graphs with girth greater than 4. We prove that z-coloring and b∗-coloring …
A linear 0-1 programming model is also presented for z-coloring of graphs. The positive …

… number of tight graphs with girth at least 8 is at least \(m(G)-1\) and characterize the graphs G
such … In a second part, we consider graphs of girth 6. We verify the conjecture of Lin et al. in …

… A b-coloring of a graph G is a proper vertex coloring of G such that each color class contains
… A coloring of G that is no b-coloring can be easily improved by choosing a color class …