# Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs

M. Salman, E.T. Baskoro, Haitze J. Broersma

Research output: Book/ReportReportOther research output

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### Abstract

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.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics Published - 2002

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1629 0169-2690

• MSC-05C40
• IR-65816
• EWI-3449
• MSC-05C85
• METIS-208263

### Cite this

Salman, M., Baskoro, E. T., & Broersma, H. J. (2002). Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs. (Memorandum; No. 1629). Enschede: University of Twente, Department of Applied Mathematics.
Salman, M. ; Baskoro, E.T. ; Broersma, Haitze J. / Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs. Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1629).
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abstract = "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.",
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author = "M. Salman and E.T. Baskoro and Broersma, {Haitze J.}",
note = "Imported from MEMORANDA",
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Salman, M, Baskoro, ET & Broersma, HJ 2002, Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs. Memorandum, no. 1629, University of Twente, Department of Applied Mathematics, Enschede.

Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs. / Salman, M.; Baskoro, E.T.; Broersma, Haitze J.

Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; No. 1629).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs

AU - Salman, M.

AU - Baskoro, E.T.

AU - Broersma, Haitze J.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

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-65816

KW - EWI-3449

KW - MSC-05C85

KW - METIS-208263

M3 - Report

T3 - Memorandum

BT - Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Salman M, Baskoro ET, Broersma HJ. Spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs. Enschede: University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1629).