More on spanning 2-connected subgraphs in truncated rectangular grid graphs

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

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Abstract

A grid graph 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. 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 languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 2002

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1637
ISSN (Print)0169-2690

Fingerprint

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

Keywords

  • MSC-05C40
  • IR-65824
  • EWI-3457
  • MSC-05C85

Cite this

Salman, M., Baskoro, E. T., & Broersma, H. J. (2002). More on spanning 2-connected subgraphs in truncated rectangular grid graphs. (Memorandum; No. 1637). Enschede: University of Twente, Department of Applied Mathematics.
Salman, M. ; Baskoro, E.T. ; Broersma, Haitze J. / More on spanning 2-connected subgraphs in truncated rectangular grid graphs. Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1637).
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Salman, M, Baskoro, ET & Broersma, HJ 2002, More on spanning 2-connected subgraphs in truncated rectangular grid graphs. Memorandum, no. 1637, University of Twente, Department of Applied Mathematics, Enschede.

More on spanning 2-connected subgraphs in truncated rectangular grid graphs. / Salman, M.; Baskoro, E.T.; Broersma, Haitze J.

Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; No. 1637).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - More on spanning 2-connected subgraphs in truncated rectangular grid graphs

AU - Salman, M.

AU - Baskoro, E.T.

AU - Broersma, Haitze J.

PY - 2002

Y1 - 2002

N2 - A grid graph 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. 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-dimensional 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-65824

KW - EWI-3457

KW - MSC-05C85

M3 - Report

T3 - Memorandum

BT - More on spanning 2-connected subgraphs in truncated rectangular grid graphs

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Salman M, Baskoro ET, Broersma HJ. More on spanning 2-connected subgraphs in truncated rectangular grid graphs. Enschede: University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1637).