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EDGE PROPERTIES OF THE 4-VALENT MULTI 3-GON GRAPHS

Jeong, Dal-Young

  • Published : 2004.07.01

Abstract

In a 4-valent multi 3-gon graph, every cut-through curve forms a simple closed circuit. Hence it is a weak arrangement of simple curves that is defined by Branko Grunbaum. In this paper, we study the edge properties of the 4-valent multi 3-gon graphs from the point of view of arrangement, and we show that they are 3 colorable.

Keywords

arrangement of curves;multi 3-gon graphs;vertex coloring

References

  1. Graph theory with applications J. A. Bondy;U. S. R. Murty
  2. Regional Conference Series in Mathematics v.10 Arrangements and spreads B. Grunbaum
  3. Memoirs of the A.M.S. Properties of planar grpahs with uniform vertex and face structure J. Malkevitch
  4. private communication J. Malkevitch