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

M. Salman, Haitze J. Broersma, C.A. Rodger

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Abstract

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.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 2003

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1700
ISSN (Print)0169-2690

Fingerprint

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

Keywords

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

Cite this

Salman, M., Broersma, H. J., & Rodger, C. A. (2003). A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs. (Memorandum; No. 1700). Enschede: University of Twente, Department of Applied Mathematics.
Salman, M. ; Broersma, Haitze J. ; Rodger, C.A. / A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs. Enschede : University of Twente, Department of Applied Mathematics, 2003. (Memorandum; 1700).
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abstract = "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.",
keywords = "MSC-05C40, EWI-3520, IR-65885, MSC-05C85",
author = "M. Salman and Broersma, {Haitze J.} and C.A. Rodger",
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Salman, M, Broersma, HJ & Rodger, CA 2003, 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.

Enschede : University of Twente, Department of Applied Mathematics, 2003. (Memorandum; No. 1700).

Research output: Book/ReportReportOther 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 -

Salman M, Broersma HJ, Rodger CA. A continuation of spanning 2-connected subgraphs in truncated rectangular grid graphs. Enschede: University of Twente, Department of Applied Mathematics, 2003. (Memorandum; 1700).