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Albertson's conjecture

Grant number: 12/16418-1
Support Opportunities:Scholarships abroad - Research Internship - Master's degree
Effective date (Start): October 01, 2012
Effective date (End): March 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Theory of Computation
Principal Investigator:Celia Picinin de Mello
Grantee:Atilio Gomes Luiz
Supervisor: R. Bruce Richter
Host Institution: Instituto de Computação (IC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: University of Waterloo, Canada  
Associated to the scholarship:12/10562-3 - Adjacent-vertex-distinguishg-total-coloring of graphs, BP.MS

Abstract

This is a research project to request a research internship abroad scholarship for Atílio Gomes Luiz, associated to process 2012/105623. It is proposed to investigate the Albertson's conjecture, which relates the chromatic number and crossing number of a graph. In 2007, Michael Albertson conjectured that if a graph G has chromatic number r, then its crossing number is at least as much as the crossing number of the complete graph with r vertices. This conjecture was confirmed be valid to r less than or equal to 16, and remains open to the other cases. The goal of this project is to investigate this conjecture for some classes of graphs. (AU)

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