Szczegóły publikacji
Opis bibliograficzny
On local irregularity conjecture for 2-multigraphs / Igor GRZELEC, Alfréd Onderko, Mariusz WOŹNIAK // Applied Mathematics and Computation ; ISSN 0096-3003 . — 2026 — vol. 514 art. no. 129832, s. 1–11. — Bibliogr. s. 11, Abstr. — Publikacja dostępna online od: 2025-11-15
Autorzy (3)
- AGHGrzelec Igor
- Onderko Alfréd
- AGHWoźniak Mariusz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 164937 |
|---|---|
| Data dodania do BaDAP | 2026-01-22 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.amc.2025.129832 |
| Rok publikacji | 2026 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Applied Mathematics and Computation |
Abstract
A multigraph in which adjacent vertices have different degrees is called locally irregular. An edge coloring of a multigraph H whose colors induce locally irregular submultigraphs is called locally irregular coloring, and the minimum number of colors of such a coloring is denoted by lir(H). In 2022, Grzelec and Woźniak conjectured that lir(2G)≤2 for every 2-multigraph 2G except 2K2 (G is the underlying simple graph). In this paper, we prove this conjecture when G is a regular, split, or special subcubic graph. We also provide constant upper bounds on lir(2G) if G is planar, or subcubic. In the proofs, we utilize special decompositions of graphs and the relation of Local Irregularity Conjecture to the well-known 1-2-3 Conjecture.
