This paper discusses a coloring game on graphs. Let k; d be non-negative integers and C a set of k colors. Two persons, Alice and Bob, alternately color the vertices of G with colors from C, withâ€¦ (More)

LetG be a connected network. Let k â‰¥ 1 be an integer. Suppose that a vertex v ofG becomes infected. A program is then installed on k-nodes not yet infected. Afterwards, the virus spreads to all itsâ€¦ (More)

We consider the following firefighter problem on a graph G = (V, E). Initially, a fire breaks out at a vertex v of G. In each subsequent time unit, a firefighter protects one vertex, and then theâ€¦ (More)

The vertex-arboricity a(G) of a graph G is the minimum number of subsets into which the set of vertices of G can be partitioned so that each subset induces a forest. It is well-known that a(G) â‰¤ 3â€¦ (More)

A proper vertex coloring of a graph G = (V, E) is acyclic if G contains no bicolored cycle. A graph G is acyclically L-list colorable if for a given list assignment L = {L(v) : v âˆˆ V }, there existsâ€¦ (More)