On the image-coloring of image-tidy graphs Original Research Article

A image-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The image-chromatic number of a graph image, denoted by image, is the maximum number image such that image admits a image-coloring with image colors. A graph image is image-continuous if it admits a image-coloring with image colors, for every image, and it is image-monotonic if image for every induced subgraph image of image, and every induced subgraph image of image. In this work, we prove that image-tidy graphs (a generalization of many classes of graphs with few induced images) are image-continuous and image-monotonic. Furthermore, we describe a polynomial time algorithm to compute theimage-chromatic number for this class of graphs.