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A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu
A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu
Computer Science Faculty Publications
A graph G is P4-sparse if no set of five vertices in G induces more than one chordless path of length three. P4-sparse graphs generalize both the class of cographs and the class of P4-reducible graphs. We give several characterizations for P4-sparse graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P4-sparse graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.