A note on Halton's conjecture

Authors:
Ondrej Sýkora;László A. Székely;Imrich Vrt'o
Affiliations:
Department of Computer Science, Loughborough University, Leicestershire LE11 3TU, UK;Department of Mathematics, University of South Carolina, Columbia, SC;Department of Informatics, Institute of Mathematics, Slovak Academy of Sciences, Dúbravská 9, 841 04 Bratislava, Slovak Republic
Venue:
Information Sciences—Informatics and Computer Science: An International Journal
Year:
2004

Citing 1
Cited 4

On the thickness of graphs of given degree

Information Sciences: an International Journal

A simulated annealing algorithm for determining the thickness of a graph

Information Sciences—Informatics and Computer Science: An International Journal
Biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method

Random Structures & Algorithms
Remarks on the thickness and outerthickness of a graph

Computers & Mathematics with Applications
A simulated annealing algorithm for determining the thickness of a graph

Information Sciences: an International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

The thickness of a graph G, is the minimum number of planar graphs, whose union is G. Halton conjectured that any graph of maximum degree d has thickness at most ⌈(d+2)/4⌉. We disprove the conjecture by showing graphs of thickness ⌈d/2⌉, for any d ≥ 5.