An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star ...
We investigate the relationship between two kinds of vertex colorings of graphs: uniquemaximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ...
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a ...
Let n(G) denote the number of vertices of a graph G and let (G) be the independence number of G, the maximum number of pairwise nonadjacent vertices of G. The Hall ratio of a grap...
We prove that coloring a 3-uniform 2-colorable hypergraph with c colors is NP-hard for any constant c. The best known algorithm [20] colors such a graph using O(n1/5 ) colors. Our...