# More on spanning 2-connected subgraphs of alphabet graphs, special classes of grid graphs

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

Research output: Book/ReportReportOther research output

## 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 English Enschede University of Twente, Department of Applied Mathematics Published - 2003

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1702 0169-2690

• MSC-05C40
• IR-65887
• EWI-3522
• MSC-05C85