We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For kdegenerate graphs with maximum degree âˆ†,â€¦ (More)

The lightness of a digraph is the minimum arc value, where the value of an arc is the maximum of the in-degrees of its terminal vertices. We determine upper bounds for the lightness of simpleâ€¦ (More)

This note generalizes the (a, b)-coloring game and the (a, b)-marking game which were introduced by Kierstead [7] for undirected graphs to directed graphs. We prove that the (a, b)-chromatic and (a,â€¦ (More)

We consider the following maker-breaker game on a bispanning graph i.e. a graph that has a partition of the edge set E into two spanning trees E1 and E2. Initially the edges of E1 are purple and theâ€¦ (More)

Using a refinement of the methods of ErdÃ¶s et al. [6] we prove that the game chromatic index of forests of maximum node degree 5 is at most 6. This improves the previously known upper bound 7 forâ€¦ (More)

A graph coloring game introduced by Bodlaender [3] as coloring construction game is the following. Two players, Alice and Bob, alternately color vertices of a given graph G with a color from a givenâ€¦ (More)

The original graph sandwich problem for a property Î , as defined by Golumbic, Kaplan, and Shamir, can be stated as follows: given two graphs G1 = (V,E1) and G2 = (V,E2), is there a graph G = (V,E)â€¦ (More)