Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers Original Research Article

Let image be a graph of nonnegative characteristic and let image and image be its girth and maximum degree, respectively. We show that image has an edge-partition into a forest and a subgraph image so that (1) image if image; (2) image if image; (3) image if either image or image does not contain 4-cycles and 5-cycles; (4) image if image does not contain image-cycles. These results are applied to find the following upper bounds for the game coloring number image of image: (1) image if image; (2) image if image; (3) image if either image or image contains no 4-cycles and 5-cycles; (4) image if image does not contain 4-cycles.