### Abstract

Original language | English |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2003 |

### Publication series

Name | Memorandum |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1700 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

- MSC-05C40
- EWI-3520
- IR-65885
- MSC-05C85

### Cite this

*A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs*. (Memorandum; No. 1700). Enschede: University of Twente, Department of Applied Mathematics.

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*A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs*. Memorandum, no. 1700, University of Twente, Department of Applied Mathematics, Enschede.

**A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs.** / Salman, M.; Broersma, Haitze J.; Rodger, C.A.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs

AU - Salman, M.

AU - Broersma, Haitze J.

AU - Rodger, C.A.

N1 - Imported from MEMORANDA

PY - 2003

Y1 - 2003

N2 - A grid graph is a finite induced subgraph of the infinite 2-dimensi-onal grid defined by $Z \times Z$ and all edges between pairs of vertices from $Z \times Z$ at Euclidean distance precisely 1. An $m\times n$-rectangular grid graph is induced by all vertices with coordinates $1$ to $m$ and $1$ to $n$, respectively. A natural drawing of a (rectangular) grid graph $G$ is obtained by drawing its vertices in $\mathbb{R}^2$ according to their coordinates. We consider a subclass of the rectangular grid graphs obtained by deleting some vertices from the corners. Apart from the outer face, all (inner) faces of these graphs have area one (bounded by a 4-cycle) in a natural drawing of these graphs. We determine which of these graphs contain a Hamilton cycle, i.e. a cycle containing all vertices, and solve the problem of determining a spanning 2-connected subgraph with as few edges as possible for all these graphs.

AB - A grid graph is a finite induced subgraph of the infinite 2-dimensi-onal grid defined by $Z \times Z$ and all edges between pairs of vertices from $Z \times Z$ at Euclidean distance precisely 1. An $m\times n$-rectangular grid graph is induced by all vertices with coordinates $1$ to $m$ and $1$ to $n$, respectively. A natural drawing of a (rectangular) grid graph $G$ is obtained by drawing its vertices in $\mathbb{R}^2$ according to their coordinates. We consider a subclass of the rectangular grid graphs obtained by deleting some vertices from the corners. Apart from the outer face, all (inner) faces of these graphs have area one (bounded by a 4-cycle) in a natural drawing of these graphs. We determine which of these graphs contain a Hamilton cycle, i.e. a cycle containing all vertices, and solve the problem of determining a spanning 2-connected subgraph with as few edges as possible for all these graphs.

KW - MSC-05C40

KW - EWI-3520

KW - IR-65885

KW - MSC-05C85

M3 - Report

T3 - Memorandum

BT - A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -