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

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

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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 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.1702
ISSN (Print)0169-2690

Keywords

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

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