Document Type

Article

Publication Date

1991

DOI

10.1016/0166-218x(91)90085-b

Publication Title

Discrete Applied Mathematics

Volume

34

Issue

1-3

Pages

151-164

Abstract

Several practical applications in computer science and computational linguistics suggest the study of graphs that are unlikely to have more than a few induced paths of length three. These applications have motivated the notion of a cograph, defined by the very strong restriction that no vertex may belong to an induced path of length three. The class of P4-extendible graphs that we introduce in this paper relaxes this restriction, and in fact properly contains the class of cographs, while still featuring the remarkable property of admitting a unique tree representation. Just as in the case of cographs, the class of P4-extendible graphs finds applications to clustering, scheduling, and memory management in a computer system. We give several characterizations for P4-extendible graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P4-extendible graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.

Comments

Elsevier open archive. Copyright © 1991 Published by Elsevier B.V. All rights reserved.

Original Publication Citation

Jamison, B., & Olariu, S. (1991). On a unique tree-representation for P4-extendible graphs. Discrete Applied Mathematics, 34(1-3), 151-164. doi:10.1016/0166-218x(91)90085-b

ORCID

0000-0002-3776-216X (Olariu)

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