Perfect k-line graphs and k-total graphs
Journal of Graph Theory
Graph classes: a survey
Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs
Journal of the ACM (JACM)
A clique-difference encoding scheme for labelled k-path graphs
Discrete Applied Mathematics
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A k-tree is either a complete graph on k vertices or a graph G = (V, E) that contains a vertex whose neighbourhood in G induces a complete graph on k vertices and whose removal results in a k-tree. We present two new subclasses of k-trees and their properties. First, we present the definition and characterization of k-path graphs, based on the concept of k-paths, that generalizes the classic concept of paths. We also introduce the simple-clique k-trees, of which the maximal outerplanar graphs and the planar 3-trees are particular cases. Based on Characterization Theorems, we show recognition algorithms for both families. Finally, we establish the inclusion relations among these new classes and k-trees.