A Tree Representation for P4-Sparse Graphs

Authors

B. Jamison, Old Dominion University
Stephan Olariu, Old Dominion UniversityFollow

Document Type

Article

Publication Date

1992

DOI

10.1016/0166-218x(92)90036-a

Publication Title

Discrete Applied Mathematics

Volume

35

Issue

2

Pages

115-129

Abstract

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.

Comments

Elsevier open archive. Copyright © 1992 Published by Elsevier B.V. All rights reserved.

Original Publication Citation

Jamison, B., & Olariu, S. (1992). A tree-representation for P₄-sparse graphs. Discrete Applied Mathematics, 35(2), 115-129. doi:10.1016/0166-218x(92)90036-a

Repository Citation

Jamison, B., & Olariu, S. (1992). A tree-representation for P₄-sparse graphs. Discrete Applied Mathematics, 35(2), 115-129. doi:10.1016/0166-218x(92)90036-a

ORCID

0000-0002-3776-216X (Olariu)