A coloring of a matroid is an assignment of colors to the elements of its ground set. We
restrict to proper colorings—those for which elements of the same color form an independent …

We define an independence system associated with simple graphs. We prove that the
independence system is a matroid for certain families of graphs, including trees, with bases …

Several games that arise from graph coloring have been introduced and studied. Let φ
denote a graph invariant that arises from such a game. If G is a graph and φ (Gx)≠ φ (G)= k …

Indicated coloring is a type of game coloring in which two players collectively color the
vertices of a graph in the following way. In each round the first player (Ann) selects a vertex …

A coloring of the ground set of a matroid is proper if elements of the same color form an
independent set. For a loopless matroid M, its chromatic number χ (M) is the minimum …

A coloring of a matroid is proper if elements of the same color form an independent set. A
theorem of Seymour asserts that a k-colorable matroid is also colorable from any lists of size …

Let $ M_1, M_2,\ldots, M_k $ be a collection of matroids on the same ground set $ E $. A
coloring $ c: E\rightarrow\{1, 2,\ldots, k\} $ is called\emph {cooperative} if for every color $ j …

Hugo Hadwiger proved that a graph that is not 3-colorable must have a K 4-minor and
conjectured that a graph that is not k-colorable must have a K k+ 1-minor. By using the …

The indicated coloring game is played on a simple graph G by two players, with a fixed set C
of colors. In each round of the game Ann indicates an uncolored vertex, and Ben colors it …

Indicated coloring of a graph G is a coloring in which there are two players Ann and Ben,
Ann picks a vertex and Ben chooses a color for this vertex. The aim of Ann is to achieve a …