### Abstract

We investigate the computational complexity of the following restricted variant of Subgraph Isomorphism: given a pair of connected graphs G=(V _{G},E _{G}) and H=(V _{H},E _{H}), determine if H is isomorphic to a spanning subgraph of G. The problem is NP-complete in general, and thus we consider cases where G and H belong to the same graph class such as the class of proper interval graphs, of trivially perfect graphs, and of bipartite permutation graphs. For these graph classes, several restricted versions of Subgraph Isomorphism such as Hamiltonian Path, Clique, Bandwidth, and Graph Isomorphism can be solved in polynomial time, while these problems are hard in general.

Original language | English |
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Pages (from-to) | 3164-3173 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 312 |

Issue number | 21 |

DOIs | |

Publication status | Published - Nov 6 2012 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics*,

*312*(21), 3164-3173. https://doi.org/10.1016/j.disc.2012.07.010

**Subgraph isomorphism in graph classes.** / Kijima, Shuji; Otachi, Yota; Saitoh, Toshiki; Uno, Takeaki.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 312, no. 21, pp. 3164-3173. https://doi.org/10.1016/j.disc.2012.07.010

}

TY - JOUR

T1 - Subgraph isomorphism in graph classes

AU - Kijima, Shuji

AU - Otachi, Yota

AU - Saitoh, Toshiki

AU - Uno, Takeaki

PY - 2012/11/6

Y1 - 2012/11/6

N2 - We investigate the computational complexity of the following restricted variant of Subgraph Isomorphism: given a pair of connected graphs G=(V G,E G) and H=(V H,E H), determine if H is isomorphic to a spanning subgraph of G. The problem is NP-complete in general, and thus we consider cases where G and H belong to the same graph class such as the class of proper interval graphs, of trivially perfect graphs, and of bipartite permutation graphs. For these graph classes, several restricted versions of Subgraph Isomorphism such as Hamiltonian Path, Clique, Bandwidth, and Graph Isomorphism can be solved in polynomial time, while these problems are hard in general.

AB - We investigate the computational complexity of the following restricted variant of Subgraph Isomorphism: given a pair of connected graphs G=(V G,E G) and H=(V H,E H), determine if H is isomorphic to a spanning subgraph of G. The problem is NP-complete in general, and thus we consider cases where G and H belong to the same graph class such as the class of proper interval graphs, of trivially perfect graphs, and of bipartite permutation graphs. For these graph classes, several restricted versions of Subgraph Isomorphism such as Hamiltonian Path, Clique, Bandwidth, and Graph Isomorphism can be solved in polynomial time, while these problems are hard in general.

UR - http://www.scopus.com/inward/record.url?scp=84865102283&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865102283&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2012.07.010

DO - 10.1016/j.disc.2012.07.010

M3 - Article

AN - SCOPUS:84865102283

VL - 312

SP - 3164

EP - 3173

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 21

ER -