| Full text | |
| Author(s): |
Botler, Fabio
;
Colucci, Lucas
;
Kohayakawa, Yoshiharu
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF GRAPH THEORY; v. 103, n. 4, p. 13-pg., 2023-03-08. |
| Abstract | |
The mod k chromatic index of a graph G is the minimum number of colors needed to color the edges of G in a way that the subgraph spanned by the edges of each color has all degrees congruent to 1 (mod k). Recently, the authors proved that the mod k chromatic index of every graph is at most 198k - 101, improving, for large k, a result of Scott. Here we study the mod k chromatic index of random graphs. We prove that for every integer k >= 2, there is C-k > 0 such that if p >= C-k n(-1) log n and n (1 - p) -> infinity as n -> infinity, then the following holds: if k is odd, then the mod k chromatic index of G (n, p) is asymptotically almost surely (a.a.s.) equal to k, while if k is even, then the mod k chromatic index of G(2n, p) (respectively, G(2n + 1, p)) is a.a.s. equal to k (respectively, k + 1). (AU) | |
| FAPESP's process: | 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics |
| Grantee: | Guilherme Oliveira Mota |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 20/08252-2 - Extremal and probabilistic problems in graph colorings |
| Grantee: | Lucas Colucci Cavalcante de Souza |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 15/11937-9 - Investigation of hard problems from the algorithmic and structural stand points |
| Grantee: | Flávio Keidi Miyazawa |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/13364-7 - Extremal and structural problems in graph theory |
| Grantee: | Cristina Gomes Fernandes |
| Support Opportunities: | Regular Research Grants |