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International Conference on Theory and Applications of Models of Computation

TAMC 2007: Theory and Applications of Models of Computation pp 115–127Cite as

A New Approach to Graph Recognition and Applications to Distance-Hereditary Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4484))

Abstract

Distance-hereditary graphs consist of the isometric graphs, and hence contain trees and cographs. First, a canonical and compact tree representation of the class is proposed. The tree representation can be constructed in linear time using two prefix trees. Usually, the prefix trees are used to maintain a set of strings. The prefix trees in our algorithm are used to maintain the neighbors for each vertex, which is new approach comparing to the other known results based on the lexicographically bread first search. Several efficient algorithms for the distance-hereditary graphs based on the canonical tree representation are proposed; linear time algorithms for graph recognition and graph isomorphism, and efficient enumeration algorithm. An efficient coding for the tree representation is also presented, which requires 4n bits for a distance-hereditary graph of n vertices, and 3n bits for a cograph. The results improve previously known upper bounds of the number of distance-hereditary graphs and cographs.

This work was partially done while the second and third authors were visiting ETH Zürich, Switzerland.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Faculty of Engineering, Gunma University, Gunma 376-8515, Japan

    Shin-ichi Nakano

  2. School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

    Ryuhei Uehara

  3. National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8430, Japan

    Takeaki Uno

Authors
  1. Shin-ichi Nakano
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  2. Ryuhei Uehara
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  3. Takeaki Uno
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Editor information

Jin-Yi Cai S. Barry Cooper Hong Zhu

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© 2007 Springer-Verlag Berlin Heidelberg

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Nakano, Si., Uehara, R., Uno, T. (2007). A New Approach to Graph Recognition and Applications to Distance-Hereditary Graphs. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_10

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  • DOI: https://doi.org/10.1007/978-3-540-72504-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72503-9

  • Online ISBN: 978-3-540-72504-6

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