Adjacent-vertex-distinguishg-total-coloring of graphs

• Grant number: 12/10562-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2012
• End date: January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Theory of Computation
• Principal Investigator: Celia Picinin de Mello
• Grantee: Atilio Gomes Luiz
• Host Institution: Instituto de Computação (IC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 12/16418-1 - Albertson's conjecture, BE.EP.MS

Abstract

This is a research project to request a master scholarship for Atílio Gomes Luiz. It is proposed to investigate a total-coloring variant called adjacent-vertex-distinguishing-total-coloring(AVD-total-coloring). Given a total-coloring, we label each vertex of a graph with the set of colors appearing on the vertex and incidentedges. When these sets are distinct for any two adjacent vertices, the total coloring is an AVD-total-coloring. The smallest number of colors for which a graph admits an AVD-total-coloring is the AVD-total-chromatic number. In the seminal article, the authors determined the AVD-total-chromatic number for few classes of graphs. Additionaly, they have conjectured a bound in terms of the maximum degree of a graph. The goal of this project is to investigate this conjecture for given positive evidence for its validity and, if possible, to determine the AVD-total-chromatic number for the graphs of some classes.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LUIZ, ATILIO G.; CAMPOS, C. N.; DE MELLO, C. P.. AVD-total-chromatic number of some families of graphs with Delta(G)=3. DISCRETE APPLIED MATHEMATICS, v. 217, n. 3, p. 628-638, JAN 30 2017. (14/16987-1, 12/10562-3)

LUIZ, ATILIO G.; CAMPOS, C. N.; DE MELLO, C. P.. AVD-total-chromatic number of some families of graphs with Delta(G)=3. DISCRETE APPLIED MATHEMATICS, v. 217, p. 11-pg., 2017-01-30. (12/10562-3, 14/16987-1)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LUIZ, Atilio Gomes. On the adjacent-vertex-distinguishing-total colouring of graphs. 2014. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Computação Campinas, SP.