Graphs and obstructions in four dimensions

  • Authors:

  • Hein van der Holst

  • Affiliations:

  • Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

For any graph G = (V, E) without loops, let C2(G) denote the regular CW-complex obtained from G by attaching to each circuit C of G a disc. We show that if G is the suspension of a flat graph, then C2(G) has an embedding into 4-space. Furthermore, we show that for any graph G in the collection of graphs that can be obtained from K7 and K3,3,1,1 by a series of ΔY- and YΔ-transformations, c2(G) cannot be embedded into 4-space.