### Abstract

Original language | English |
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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. | 1702 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

- MSC-05C40
- IR-65887
- EWI-3522
- MSC-05C85

### Cite this

*More on spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs*. (Memorandum; No. 1702). Enschede: University of Twente, Department of Applied Mathematics.

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*More on spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs*. Memorandum, no. 1702, University of Twente, Department of Applied Mathematics, Enschede.

**More on spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs.** / Salman, M.; Broersma, Haitze J.; Rodger, C.A.

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

TY - BOOK

T1 - More on spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs

AU - Salman, M.

AU - Broersma, Haitze J.

AU - Rodger, C.A.

PY - 2003

Y1 - 2003

N2 - A grid graph $G$ is a finite induced subgraph of the infinite 2-dimensional grid defined by $Z \times Z$ and all edges between pairs of vertices from $Z \times Z$ at Euclidean distance precisely 1. A natural drawing of $G$ is obtained by drawing its vertices in $\mathbb{R}^2$ according to their coordinates. Apart from the outer face, all (inner) faces with area exceeding one (not bounded by a 4-cycle) in a natural drawing of $G$ are called the holes of $G$. We define 26 classes of grid graphs called alphabet graphs, with no or a few holes. We determine which of the alphabet 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 alphabet graphs.

AB - A grid graph $G$ is a finite induced subgraph of the infinite 2-dimensional grid defined by $Z \times Z$ and all edges between pairs of vertices from $Z \times Z$ at Euclidean distance precisely 1. A natural drawing of $G$ is obtained by drawing its vertices in $\mathbb{R}^2$ according to their coordinates. Apart from the outer face, all (inner) faces with area exceeding one (not bounded by a 4-cycle) in a natural drawing of $G$ are called the holes of $G$. We define 26 classes of grid graphs called alphabet graphs, with no or a few holes. We determine which of the alphabet 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 alphabet graphs.

KW - MSC-05C40

KW - IR-65887

KW - EWI-3522

KW - MSC-05C85

M3 - Report

T3 - Memorandum

BT - More on spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -