Abstract
| Original language | English |
|---|---|
| Place of Publication | Enschede |
| Publisher | University of Twente, Department of Applied Mathematics |
| Publication status | Published - 2003 |
Publication series
| Name | Memorandum |
|---|---|
| Publisher | Department of Applied Mathematics, University of Twente |
| No. | 1700 |
| ISSN (Print) | 0169-2690 |
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Keywords
- MSC-05C40
- EWI-3520
- IR-65885
- MSC-05C85
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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/Report › Report › Other 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 -