Title: Acyclic Edge-Colouring of Graphs
Data: 17 de maio de 2024 – sexta-feira – 15h - Auditório Jacy Monteiro, IME/USP
Student: Ariana Maite Quispe Porras

Abstract: A proper edge-colouring of a graph G is called acyclic if there are no bichromatic cycles in G. The acyclic chromatic index of G, denoted by a’(G), is the smallest number k such that G admits an acyclic edge colouring using k colours. Fiamčik (1978) and Alon et al. (2001) independently conjectured that a’(G) ≤ Δ(G) + 2 for any simple graph G. This conjecture is well known as the Acyclic Edge-Colouring Conjecture (AECC). Currently, the best known upper bound for an arbitrary graph is 3.569(Δ(G) - 1), proved by Fialho et al. (2020). It was proved using a modification of the method described by Giotis et al. (2017). Furthermore, the AECC was proved for graphs with Δ(G) ≤ 4 and for complete bipartite graphs K_{p,p} when p is prime. The main objective of this research project is to study the AECC for those cases, simplify the existing proofs and try to prove the AECC for Δ(G) = 5.