A Steiner triple system has a bicoloring with m color classes if the points are partitioned into m subsets and the three points in every block are contained in exactly two of the ...
Charles J. Colbourn, Jeffrey H. Dinitz, Alexander ...
We call a coloring of the edge set of a graph G a b-bounded coloring if no color is used more than b times. We say that a subset of the edges of G is rainbow if each edge is of a ...
Tom Bohman, Alan M. Frieze, Oleg Pikhurko, Cliffor...
For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by prec...
Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct fro...
In this paper, a structural theorem about toroidal graphs is given that strengthens a result of Borodin on plane graphs. As a consequence, it is proved that every toroidal graph w...