Equivalences and the complete hierarchy of intersection graphs of paths in a tree Original Research Article

An image-representation of a graph image consists of a collection of subtrees of a tree image, where each subtree corresponds to a vertex in image, such that (i) the maximum degree of image is at most image, (ii) every subtree has maximum degree at most image, (iii) there is an edge between two vertices in the graph image if and only if the corresponding subtrees have at least image vertices in common in image. The class of graphs that have an image-representation is denoted by image. It is well known that the class of chordal graphs corresponds to the class [3, 3, 1]. Moreover, it was proved by Jamison and Mulder that chordal graphs correspond to orthodox-[3, 3, 1] graphs defined below.