# Spanning 2-connected subgraphs in truncated rectangular grid graphs

A.N.M. Salman, E.T. Baskoro, H.J. Broersma

Research output: Book/ReportReportOther research output

### Abstract

A grid graph is a finite induced subgraph of the infinite 2-dimensio- nal 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.
Original language English Enschede University of Twente, Department of Applied Mathematics 8 Published - 2002

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1630 0169-2690

### Fingerprint

Grid Graph
Subgraph
Graph in graph theory
Cycle
Hamilton Cycle
Induced Subgraph
Euclidean Distance
Face
Grid
Drawing

• MSC-05C40
• IR-65817
• EWI-3450
• MSC-05C85
• METIS-208264

### Cite this

Salman, A. N. M., Baskoro, E. T., & Broersma, H. J. (2002). Spanning 2-connected subgraphs in truncated rectangular grid graphs. (Memorandum; No. 1630). Enschede: University of Twente, Department of Applied Mathematics.
Salman, A.N.M. ; Baskoro, E.T. ; Broersma, H.J. / Spanning 2-connected subgraphs in truncated rectangular grid graphs. Enschede : University of Twente, Department of Applied Mathematics, 2002. 8 p. (Memorandum; 1630).
@book{474ce655e17c40a49c95eaaf1bda33ba,
title = "Spanning 2-connected subgraphs in truncated rectangular grid graphs",
abstract = "A grid graph is a finite induced subgraph of the infinite 2-dimensio- nal 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.",
keywords = "MSC-05C40, IR-65817, EWI-3450, MSC-05C85, METIS-208264",
author = "A.N.M. Salman and E.T. Baskoro and H.J. Broersma",
note = "Imported from MEMORANDA",
year = "2002",
language = "English",
series = "Memorandum",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1630",

}

Salman, ANM, Baskoro, ET & Broersma, HJ 2002, Spanning 2-connected subgraphs in truncated rectangular grid graphs. Memorandum, no. 1630, University of Twente, Department of Applied Mathematics, Enschede.

Spanning 2-connected subgraphs in truncated rectangular grid graphs. / Salman, A.N.M.; Baskoro, E.T.; Broersma, H.J.

Enschede : University of Twente, Department of Applied Mathematics, 2002. 8 p. (Memorandum; No. 1630).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Spanning 2-connected subgraphs in truncated rectangular grid graphs

AU - Salman, A.N.M.

AU - Broersma, H.J.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

N2 - A grid graph is a finite induced subgraph of the infinite 2-dimensio- nal 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-dimensio- nal 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 - IR-65817

KW - EWI-3450

KW - MSC-05C85

KW - METIS-208264

M3 - Report

T3 - Memorandum

BT - Spanning 2-connected subgraphs in truncated rectangular grid graphs

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Salman ANM, Baskoro ET, Broersma HJ. Spanning 2-connected subgraphs in truncated rectangular grid graphs. Enschede: University of Twente, Department of Applied Mathematics, 2002. 8 p. (Memorandum; 1630).