Near-homogeneous spherical Latin bitrades

Nicholas J. Cavenagh

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 3, page 313-328
  • ISSN: 0010-2628

Abstract

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A planar Eulerian triangulation is a simple plane graph in which each face is a triangle and each vertex has even degree. Such objects are known to be equivalent to spherical Latin bitrades. (A Latin bitrade describes the difference between two Latin squares of the same order.) We give a classification in the near-regular case when each vertex is of degree 4 or 6 (which we call a near-homogeneous spherical Latin bitrade, or NHSLB). The classification demonstrates that any NHSLB is equal to two graphs embedded in hemispheres glued at the equator, where each hemisphere belongs to one of nine possible types, each of which may be described recursively.

How to cite

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Cavenagh, Nicholas J.. "Near-homogeneous spherical Latin bitrades." Commentationes Mathematicae Universitatis Carolinae 54.3 (2013): 313-328. <http://eudml.org/doc/260588>.

@article{Cavenagh2013,
abstract = {A planar Eulerian triangulation is a simple plane graph in which each face is a triangle and each vertex has even degree. Such objects are known to be equivalent to spherical Latin bitrades. (A Latin bitrade describes the difference between two Latin squares of the same order.) We give a classification in the near-regular case when each vertex is of degree $4$ or $6$ (which we call a near-homogeneous spherical Latin bitrade, or NHSLB). The classification demonstrates that any NHSLB is equal to two graphs embedded in hemispheres glued at the equator, where each hemisphere belongs to one of nine possible types, each of which may be described recursively.},
author = {Cavenagh, Nicholas J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {planar Eulerian triangulation; Latin bitrade; Latin square; Latin bitrade; Eulerian triangulation; planar graph},
language = {eng},
number = {3},
pages = {313-328},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Near-homogeneous spherical Latin bitrades},
url = {http://eudml.org/doc/260588},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Cavenagh, Nicholas J.
TI - Near-homogeneous spherical Latin bitrades
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 3
SP - 313
EP - 328
AB - A planar Eulerian triangulation is a simple plane graph in which each face is a triangle and each vertex has even degree. Such objects are known to be equivalent to spherical Latin bitrades. (A Latin bitrade describes the difference between two Latin squares of the same order.) We give a classification in the near-regular case when each vertex is of degree $4$ or $6$ (which we call a near-homogeneous spherical Latin bitrade, or NHSLB). The classification demonstrates that any NHSLB is equal to two graphs embedded in hemispheres glued at the equator, where each hemisphere belongs to one of nine possible types, each of which may be described recursively.
LA - eng
KW - planar Eulerian triangulation; Latin bitrade; Latin square; Latin bitrade; Eulerian triangulation; planar graph
UR - http://eudml.org/doc/260588
ER -

References

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